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2-category 2-category-theory abelian-categories accessible adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology newpage nlab noncommutative noncommutative-geometry number number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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- Discussion Type
- discussion topicgaugino
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 19th 2011

stub for gaugino

- Discussion Type
- discussion topicconnection on a double category
- Category Latest Changes
- Started by FinnLawler
- Comments 1
- Last comment by FinnLawler
- Last Active Apr 18th 2011

Stubby little page for connection on a double category.

- Discussion Type
- discussion topicadjoint n-tuple
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Apr 14th 2011

Zoran has created adjoint triple, I have added adjoint quadruple

- Discussion Type
- discussion topicformally unramified morphism
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Apr 14th 2011

I have split off formally unramified morphism from unramified morphism. Then I added the general-abstract topos theoretic characterization, by essentially copy-and-pasting the discussion from formally smooth morphism (and replacing epimorphisms by monomorphisms)

- Discussion Type
- discussion topicformal groupoid
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 13th 2011

stub for formal groupoid. Just collecting references so far.

- Discussion Type
- discussion topicQ-categories (and cohesive toposes)
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by zskoda
- Last Active Apr 13th 2011

After Zoran had emphasized it for years without me ever really looking into it, now I have finally read the beginning of Kontsevich-Rosenberg’s article on “Q-categories” in more details… and was struck:

their notion of “generalized sheaves” is essentially nothing but the kind of condition that Lawvere considered in cohesive toposes $(u_! \dashv u^* \dashv u_* \dashv u^!) : T \to S$. More precisely, Lawvere considered the objects $x$ for which the canonical morphism $u_* x \to u_! x$ is an isomorphism. What Kontsevich-Rosenberg call generalized sheaves are those objects for which the

*other*canonical morphism is an isomorphism: $u^* x \to u^! x$.There are mainly two kinds of applications in Kontsevich-Rosenberg:

the original one was to find the right notion of sheaves over formal duals of non-commutative algebras. Apparently Rosenberg is fond of the insight that for a suitable cohesive presheaf topos (my words of course) the right condition is that $u^* x \to u^! x$ is an iso.

Apparently (if I remember correctly what Zoran told me) Kontsevich added the observation that formal smoothness and hence infinitesimal thickening is naturally described in this context. Now that I looked through it, I realize that what they talk about in this context is really pretty much exactly what I axiomatized as infinitesimal cohesion.

So I am happy: at once now the entire 79 page article by Kontsevich-Rosenberg turns out to be a great resource of examples and applications of cohesive topos technology! Notably they shed more light on the role of those infamous

*extra axioms*that involve the two canoical natural transformations that come with any cohesive topos.For that reason I have now begun expanding the $n$Lab entry Q-category that Zoran once started

- Discussion Type
- discussion topictopologizing subcategory
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active Apr 13th 2011

This was the query in topologizing subcategory which I summarized shortly:

Mike: Where does the word ’topologizing’ come from?

Zoran Skoda: I am not completely sure anymore, but I think it is from ring theory, where people looked at the localizations at topologizing categories. There exist some topologies on various sets of ideals like Jacobson topology, so it is something of that sort in the language of subcategories instead of the language of filters of ideals. I’ll consult old references like Popescu, maybe I recall better. In any case it is pretty standard and has long history in usage: both classical and modern. No, it is not in Popescu…old related term is in fact talking about topologizing filters of ideals in a ring, so that must be the source…for example, the classical algebra by Faith, vol I, page 520 defines when the set of right ideals is topologizing. I am not good with that notion, but I can make an entry with quotation to be improved later.

- Discussion Type
- discussion topicseparable functor, S-category
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Apr 13th 2011

New microstubs S-category, separable coring and finally some substantial material at separable functor at last. The monograph by Caenapeel, Militaru and Zhu listed at separable functor studies Frobenius functors and separable functors in parallel; there are relations in a number of interesting situations. Frobenius functors are those where left and right adjoint are the same (hence in particular we have adjoint n-tuple for every $n$). Separable is a notion which is about certain spliting condition. This spliting is of the kind as spliting in Galois theory, I mean the Grothendieck’s version of classical Galois theory involves separable algebras at one side of Galois equivalence.

S-category due Tomasz Brzeziński is a formalism something similar to Q-categories of Alexander Rosenberg. Tomasz studies formal smoothness and separability in the setup of abelian categories, motivated by corings, Hopf algebras and similar applications. I would guess that understanding those could be useful into better understanding the Galois theory in cohesive topos, but I do not know.

I also created Maschke’s theorem which is one of the motivations for separable functors.

- Discussion Type
- discussion topicformally smooth morphism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 12th 2011

I have expanded the entry formally smooth morphism:

I have first of all added the general-abstract formalization by Kontsevich-Rosenberg, taking the liberty of polishing it a bit from Q-category language to genuine (cohesive) topos-theoretic language and making contact with the notion of infinitesimal cohesion .

Then I added their theorems about how the general abstract topos-theoretic definitions do reproduce the traditional explicit notions.

Except for one clause : in prop. 5.8.1 of

*Noncommutative spaces*they show that the correct notion of formal smoothness for morphisms is reproduced in the non-commutative case (via the relative Cuntz-Quillen condition). But for the commutative case I see the corresponding statement only for objects (in section 4.1) not for morphisms.Zoran, do you know if they also discuss the relative version in the commutative case? Maybe it’s trivial, I haven’t thought it through yet.

- Discussion Type
- discussion topicMore knot theory stuff
- Category Latest Changes
- Started by Andrew Stacey
- Comments 4
- Last comment by Andrew Stacey
- Last Active Apr 11th 2011

Expanded Vassiliev invariant, started Kontsevich integral, did a bit of reorganisation on knot theory (in particular, linking to more pages).

In case anyone’s wondering, there was a book put on the arXiv a couple of days ago touting itself as an introduction to Vassiliev invariants. I’m reading through it and taking notes as I go. I left in a bit of a rush today so the formatting of the Kontsevich integral went a bit haywire, and I made a statement on the Vassiliev invariant page that I know I didn’t say quite right.

In the arXiv book, Vassiliev invariants are introduced first using the Vassiliev skein relations, not their “proper” way (which I haven’t gotten to yet so I don’t know it). The formula looked very like a boundary map on a complex, but I think it has to be a cubical complex rather than a simplicial one. Only it isn’t the full boundary map, rather a partial boundary map (going to opposite faces), but I didn’t get it straight in my head until later. But now I think I’m going to wait until I read the bit about the

*true*definition - which I guess will be something like this - before correcting it (unless anyone gets there before me, of course).Drew a few more SVGs relevant for knots as well. The code for producing the trefoil knot is very nice now, though I say so myself!

- Discussion Type
- discussion topicsupergravity Lie 6-algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 11th 2011

added to supergravity Lie 6-algebra a brief discussion of how the equations of motion of 11-d supergravity encode precisely the “rheonomic” $\infty$-connections with values in the supergravity Lie 6-algebra.

- Discussion Type
- discussion topicPaolo Salvatore
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Apr 10th 2011

Stub for Paolo Salvatore.

- Discussion Type
- discussion topicframed little disk operad
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Apr 10th 2011

created framed little disk operad

- Discussion Type
- discussion topicGiansiracusa
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Apr 9th 2011

I created a stub for Jeff Giansiracusa.

- Discussion Type
- discussion topicconstructive Riesz representation theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 8th 2011

reference for constructive proof of Riesz representation theorem

- Discussion Type
- discussion topicconstructive Gelfand duality theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 8th 2011

Bas Spitters has kindly pointed out to me that the proof by Banaschewski and Mulvey of Gelfand duality is not actually constructive, as it invokes Barr’s theorem, and that he has a genuine constructive and also simpler proof with Coquand. I have added that to the refrences at constructive Gelfand duality theorem

- Discussion Type
- discussion topichomotopy colimit
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Apr 8th 2011

I added to Quillen bifunctor as a further "application" the discussion of Bousfield-Kan type homotopy colimits.

At some point I want to collect the material on homotopy (co)limits currently scattered at Bousfield-Kan map at weighted limit and now at Quillen bifunctor into one coherent entry.

- Discussion Type
- discussion topicbilinear form
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Apr 7th 2011

it has annoyed me for a long time that bilinear form did not exist. Now it does. But not much there yet.

- Discussion Type
- discussion topicTuraev
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Urs
- Last Active Apr 6th 2011

I have created a (stubby) entry for Turaev. It needs more links.

- Discussion Type
- discussion topiccompact Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Apr 6th 2011

stub for compact Lie algebra

- Discussion Type
- discussion topicCrossed G-algebras
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Apr 5th 2011

I have started a stub on crossed G-algebras

- Discussion Type
- discussion topicendomorphism infinity-Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Apr 5th 2011

- Discussion Type
- discussion topiccohomology operation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2011

created cohomology operation, just to record the two references that they are discussing curently on the ALG-TOP list

- Discussion Type
- discussion topicWrithe
- Category Latest Changes
- Started by Andrew Stacey
- Comments 1
- Last comment by Andrew Stacey
- Last Active Mar 31st 2011

Couple of minor knot changes: writhe is new, and I added the missing diagram (and some redirects) to framed link.

- Discussion Type
- discussion topicEquivalence classes
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Mar 29th 2011

Both equivalence class and partition used to redirect to equivalence relation, but neither term even appeared there. I removed the redirects and wrote equivalence class (but not partition).

By the way, I wrote this article entirely on my new phone (Android); I’m kind of getting the hang of this!

- Discussion Type
- discussion topicsuper L-oo algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 29th 2011

have created super L-infinity algebra

- Discussion Type
- discussion topicnoncommutative Gelfand-Naimark theorem
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Mar 29th 2011

I need to be looking again into the subject of the Gelfand-Naimark theorem for noncommutative $C^*$-algebras $A$ regarded as commutative $C^*$-algebras in the copresheaf topos on the poset of commutative subalgebras of $A$, as described in

Heunen, Landsman, Spitters, A topos for algebraic quantum theory.

While it seems clear that something relevant is going on in these constructions, I am still trying to connect all this better to other topos-theoretic descriptions of physics that I know of.

Here is just one little observation in this direction. Not sure how far it carries.

If I understand correctly, we have in particular the following construction: for $\mathcal{H}$ a Hilbert space and $B(\mathcal{H})$ its algebra of bounded operators, let $A : \mathcal{O}(X) \to CStar$ be a local net of algebras on some Minkowski space $X$. landing (without restriction of generality) in subalgebras of $B(\mathcal{H})$.

By the internal/noncommutative Gelfand-Naimark theorem we have that each noncommutative $C^*$-algebra that $A$ assigns to an open subset corresponds bijectively to a locale internal to the topos $\mathcal{T}_{B(\mathcal{H})}$ of copresheaves on the commutative subalgebras of $B(\mathcal{H})$.

So using this, our Haag-Kastler local net becomes an internal-locale-valued presheaf

$A : \mathcal{O}(X)^{op} \to Loc(\mathcal{T}_{B(\mathcal{H})}) \,.$So over the base topos $B(\mathcal{H})$ this is a “space-valued presheaf”. we could think about generalizing this to $\infty$-presheaves, probably (though I’d need to think about if we really get there given that the locales need not come from actual spaces). The we could think about if this generalization dually corresponds indeed to the “higher order local nets” such as factorization algebras.

Just a very vague thought. Have to run now.

- Discussion Type
- discussion topicnilradical
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 29th 2011

created nilradical

- Discussion Type
- discussion topicThe long exact sequence of a pair
- Category Latest Changes
- Started by domenico_fiorenza
- Comments 3
- Last comment by zskoda
- Last Active Mar 28th 2011

do we already have this in nLab? it seems that the long exact sequence in cohomology

$\cdots \to H^n(X,Y;A)\to H^n(X,A)\to H^n(Y,A) \to H^{n+1}(X,Y;A)\to \cdots$for an inclusion $Y\hookrightarrow X$ should have the following very simple and natural interpretation: for a morphism $f:Y\to X$ in a (oo,1)-topos $\mathbf{H}$ and a coefficient object $A$ together with a fixed morphism $\varphi:Y\to A$, consider the induced morphism $f^*:\mathbf{H}(X,A)\to \mathbf{H}(Y,A)$ and take its (homotopy) fiber over the point $*\stackrel{\varphi}{\to}\mathbf{H}(Y,A)$. In particular, when the coefficient object $A$ is pointed, we can consider the case where $\varphi:Y\to A$ is the distinguished point of $\mathbf{H}(Y,A)$. In this case the homotopy fiber one is considering should be denoted $\mathbf{H}(X,Y;A)$ and is the hom-space for the cohomology of the pair $(X,Y)$ with coefficients in $A$ (here one should actually make an explicit reference to the morphism $f:Y\to X$ in the notation, unless it is “clear” as in the case of the inclusion of the classical cohomology of a pair). then, for a deloopable coefficients object $A$, the long exact sequence in cohomology should immediately follow from the fiber sequence

$\array{ \mathbf{H}(X,Y;A) &\to& \mathbf{H}(X,A) \\ \downarrow && \downarrow \\ * &\to& \mathbf{H}(Y,A) }$

- Discussion Type
- discussion topicsupergravity Lie 3-algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 24th 2011

created supergravity Lie 3-algebra

- Discussion Type
- discussion topicsuperpoint
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 23rd 2011

created superpoint

- Discussion Type
- discussion topicGerstenhaber-Schack cohomology
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active Mar 23rd 2011

Tim has touched a bit entries on Drinfel’d twist and the more general bialgebra cocycle a la Shahn Majid and I have added another kind of bialgebra cocycles, namely those defining the Gerstenhaber-Schack cohomology. I added a tag gebra to this post (cogebras, bigebras etc.).

- Discussion Type
- discussion topicPhyics
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Mar 19th 2011

Can someone with more access than I have do a search and replace for Phyics. I have changed two entries to Physics (which I assume is correct :-)) but as it is not an important typo and there are five or six other occurrences a block replace is probably easy to do.

- Discussion Type
- discussion topicalgebra over a monad
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 17th 2011

I wanted to archive a pointer to Isbells

*Generic algebras*somewhere on the nLab, and now did so in algebra over a monad. But it is sitting a bit lonesomely there now by itself in the References-section…

- Discussion Type
- discussion topicvanishing cycle
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Mar 17th 2011

Big stub (lots of references and links) for vanishing cycle and related microstub for Milnor fiber. Some related changes at intersection cohomology, perverse sheaf.

- Discussion Type
- discussion topicnormal operator
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Mar 16th 2011

created a stub for normal operator and noticed/remembered that Tim van Beek had once created the beginning of an entry spectral theorem that he ended with an empty section on the version for normal operators. If we are lucky he will come back some day and complete this, but it looks like he won’t. Maybe somebody else feels inspired to work on this entry.

- Discussion Type
- discussion topicaffine morphism
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Mar 16th 2011

New entry affine morphism (redirecting also affine morphism of schemes) and a related post at MathOverflow, linked there. Expansion of the material at affine scheme including few words on relative affine schemes and on fundamental theorem on morphisms of schemes.

- Discussion Type
- discussion topicDeligne conjecture
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Mar 11th 2011

have split off Deligne conjecture from Hochschild cohomology and expanded it. Various references only indicated by author name, still need to fill in publication informaiton

- Discussion Type
- discussion topicmodel structure on dg-modules
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Mar 11th 2011

I have created an entry model structure on dg-modules in order to record some references and facts.

I think using this I now have one version of the statement at derived critical locus (schreiber) that is fully precise. But I am still trying to see a better way. This is fiddly, because

contrary to what one might expect, thre is not much at all in the literature on general properties homotopy limits/colimits in dg-geometry;

and large parts of the standard toolset of homotopy theory of oo-algebras does not apply:

the fact that we are dealing with

*commutative*dg-algebras makes all Schwede-Shipley theory not applicable,the fact that we are dealing with oo-algebras in chain complexes makes all Berger-Moerdijk theory not apply;

and finally the fact that we are dealing with dg-algebras under another dg-algebra makes Hinich’s theory not apply!

That doesn’t leave many tools to fall back to.

- Discussion Type
- discussion topicEhlers
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Mar 10th 2011

I have created an entry on Phil Ehlers since Stephen Gaito has kindly scanned Phil’s MSc Thesis from 1991. (Phil’s PhD thesis was already on the Lab. The MSc is also there now.)

- Discussion Type
- discussion topicNotes of Utrecht talk
- Category Latest Changes
- Started by domenico_fiorenza
- Comments 25
- Last comment by Tim_Porter
- Last Active Mar 8th 2011

I’ve started writing the notes of the talk I’ll be giving in Utrecht next week. They are here

- Discussion Type
- discussion topichomological perturbation theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 8th 2011

added references to homological perturbation theory

- Discussion Type
- discussion topicseminar on derived critical loci
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by zskoda
- Last Active Mar 7th 2011

with only about a month delay, I am starting now on my personal web a page

*Seminar on derived critical loci (schreiber)*

- Discussion Type
- discussion topiccomplex structure
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Tim_Porter
- Last Active Mar 7th 2011

stub for complex structure

- Discussion Type
- discussion topicmultivector field
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Mar 4th 2011

added to multivector field further references on how the divergenc/BV operator is the dual of the de Rham differential.

Domenico, could you tell me if you think that the following statement is correct?

in full abstractness, the content of Lagrangian BV is this:

we

start with a configuration space of sorts

and assume we have a fixed isomorphism between its Hochschild cohomology and Hochshcild homology, which we think of as an iso between its differential forms and its multivector fields induced by a volume form (which it is for finite dimensional spaces);

then we think of an action functional times a volume form on our configuration space as a closed differential form $\exp(i S) vol$, hence as an element in the Hochschild homology that is also in the cyclic homology

and then use the above isomorphism to think of this equivalently an element in Hochschild cohomology, being a cocycle in cyclic cohomology.

the cyclic differential is the BV-operator and the closure condition is the “master equation” $\Delta \exp(i S) = 0$;

the fact that Lagrangian BV is controled by BV-algebra and hence, by Getzler’s theorem, by algebra over the homology of the little framed disk operad now follows from the fact that Hochschild homology of our space is given by the derived loop space.

Is that right? Is that the NiceStoryAboutLagrangianBV™? If so, is this written out in this fashion explicitly somewhere?

- Discussion Type
- discussion topicKoszul-Tate resolution
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 3rd 2011

stub for Koszul-Tate resolution

- Discussion Type
- discussion topicvariational calculus on diffeological spaces
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Mar 3rd 2011

I have added to variational calculus a definition of critical loci of functionals, hence a definition of Euler-Lagrange equations, in terms of diffeological spaces. It’s a very natural definition which is

*almost*explicit in Patrick Iglesias-Zemmour’s book, only that he cannot make it fully explicit since the natural formulation involves the sheaf of forms $\Omega^1_{cl}(-)$ which is not concrete and hence not considered in that book.I was hoping I would find in his book the proof that the critical locus of a function on a diffeological space defined this was coincides with the “EL-locus” – it certainly contains it, but maybe there is some discussion necessary to show that it is not any larger – but on second reading it seems to me that the book also only observes the inclusion.

- Discussion Type
- discussion topicTarski’s Two Approaches to Modal Logic
- Category Latest Changes
- Started by Tim_Porter
- Comments 7
- Last comment by Tim_Porter
- Last Active Feb 28th 2011

This is a ’latest changes’, but for the Café rather than the backroom! Can David C (or someone) fix the link that does not work to Steve Awodey’s paper (It should be http://www.andrew.cmu.edu/user/awodey/preprints/FoS4.phil.pdf).

- Discussion Type
- discussion topicStructures de Dérivabilité
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 28th 2011

created Reference-entry Structures de Dérivabilité

- Discussion Type
- discussion topicpresymplectic structure
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 26th 2011

stub for presymplectic structure (just to record a reference on presymplectic reduction)

- Discussion Type
- discussion topicquotient space
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by TobyBartels
- Last Active Feb 24th 2011

Stub for quotient space.

- Discussion Type
- discussion topicKhovanov homology
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active Feb 24th 2011

have created an entry Khovanov homology, so far containing only some references and a little paragraph on the recent advances in identifying the corresponding TQFT. I have also posted this to the $n$Café here, hoping that others feel inspired to work on expanding this entry

- Discussion Type
- discussion topicMilnor mu-bar invariants
- Category Latest Changes
- Started by Andrew Stacey
- Comments 4
- Last comment by Tim_Porter
- Last Active Feb 22nd 2011

I wanted to understand Milnor’s paper on Link Groups, so I basically rewrote the main bits in to Milnor mu-bar invariants. (I don’t understand the difference between $\mu$-invariants and $\bar{\mu}$-invariants, but I was only working on the original paper so presumably haven’t gotten that far yet.)

I even put a TOC in so Urs will be happy!

- Discussion Type
- discussion topicLisbon meeting notes
- Category Latest Changes
- Started by Tim_Porter
- Comments 10
- Last comment by Tim_Porter
- Last Active Feb 22nd 2011

I have just added a link to the notes that I prepared for the Lisbon meeting on my personal page. I would love to have some feedback, and in particular suggestions for incorporating some more of this in the nLab. The new material also forms part of the extended version of the Menagerie (which is now topping 800 pages.)

- Discussion Type
- discussion topicString 2-group
- Category Latest Changes
- Started by Guest
- Comments 7
- Last comment by Urs
- Last Active Feb 21st 2011

- At string 2-group it is claimed that the sequence of classifying spaces ending --> BSO(n) --> BO(n) is the Whitehead tower of O(n). Also mentioned is the version for smooth infinity groupoids (so I assume it is Urs who put that there). It is certainly not true that the sequence of classifying spaces so stated is the Whitehead tower for O(n), but the details for groups considered as one-object infinity groupoids are open to interpretation, so I haven't changed anything. Just a heads up.

-David Roberts

- Discussion Type
- discussion topiclocally equi-connected space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 21st 2011

stub for locally equi-connected space

- Discussion Type
- discussion topicimpredicativity
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Feb 19th 2011

I have added a brief note about type-theoretic polymorphism to the list of impredicative axioms at predicative mathematics.

- Discussion Type
- discussion topicstructured ring spectrum
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 18th 2011

I see there is quite a bit of room for improvement of the $n$Lab material on ring spectra.

I noticed that smash product of ring spectra still pointed to a stub entry, while in parallel we have a fairly good beginning of a genuine entry at symmetric monoidal smash product of spectra. So I blanked the former and made it redirect to the latter.

I also made structured ring spectrum a redirect to this for the moment.

- Discussion Type
- discussion topiceffects of foundations
- Category Latest Changes
- Started by DavidRoberts
- Comments 4
- Last comment by DavidRoberts
- Last Active Feb 16th 2011

At effects of foundations on “real” mathematics I’ve put in the example of Fermat’s last theorem as being potentially derivable from PA, and pointed to two articles by McLarty on this topic.

(Edit: the naive wikilink to the given page breaks, due to the ” ” pair)

- Discussion Type
- discussion topicQuiver: discussion; Directed graph: discussion
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Feb 15th 2011

I’ve removed old discussion from quiver and directed graph. They can be found at revision #20 and revision #24, respectively.