Not signed in (Sign In)

A discussion forum about contributions to the nLab wiki and related areas of mathematics, physics, and philosophy.

Want to take part in these discussions? Sign in if you have an account, or apply for one below

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundle bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics planar 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 stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

- Discussion Type
- discussion topicnatural isomorphism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 26th 2010

edited natural isomorphism a bit more

- Discussion Type
- discussion topicdagger-categories
- Category Latest Changes
- Started by John Baez
- Comments 2
- Last comment by Eric
- Last Active Apr 26th 2010

In preparation for week296 I corrected the definition of dagger-compact category, since it was missing some coherence laws. The most convenient way to include these was to add a page containing Selinger’s definition of symmetric monoidal dagger-category . This in turn forced me to add pages containing definitions of associator, unitor, braiding and unitary morphism. Some of my links between these pages are afflicted by the difficulty of getting daggers to appear in names of pages. Maybe a lab elf can improve them.

Hmm, html links didn’t work here, so I’m trying textile.

- Discussion Type
- discussion topicgeometrodynamics
- Category Latest Changes
- Started by Eric
- Comments 5
- Last comment by Eric
- Last Active Apr 25th 2010

Created a stub with some references for geometrodynamics.

- Discussion Type
- discussion topicorientation in generalized cohomology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 24th 2010

- Discussion Type
- discussion topicZeidler
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active Apr 24th 2010

I have moved the personal data on Eberhard Zeidler from QFT entry to his own new-created entry.

- Discussion Type
- discussion topic[[Dmitry Tamarkin]]
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Apr 23rd 2010

Dmitry Tamarkin and Gonçalo Tabuada; 2 new references at microlocal analysis.

- Discussion Type
- discussion topicMayer-Vietoris sequence
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 22nd 2010

cerated at fibration sequence an Examples-subsection on the special case of Mayer-Vietoris sequences. From the nPOV, where it becomes a triviality, of course.

- Discussion Type
- discussion topicrationalization
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Apr 22nd 2010

created rationalization even though it overlaps with the material at rational topological space

- Discussion Type
- discussion topicMathematical Reviews
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by DavidRoberts
- Last Active Apr 21st 2010

with the URL code for Relay Station, useful for linking from $n$lab

- Discussion Type
- discussion topichomotopy BV-algebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Apr 20th 2010

After having received an email from Bruno Valette I have now at least added a minimum of references to the stub entry homotopy BV-algebra.

- Discussion Type
- discussion topicGaudin model
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Apr 20th 2010

Gaudin integrable model as a special case of Hitchin integrable system, and expansion of entry Branislav Jurčo.

- Discussion Type
- discussion topicequivariant localization
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Apr 20th 2010

equivariant localization (only good references and links for now) and Michael Atiyah

- Discussion Type
- discussion topicpseudoalgebras
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Apr 19th 2010

Created pseudoalgebra for a 2-monad as a place to store something I just noticed about normalization, and a related stub at isocofibration.

- Discussion Type
- discussion topicunbounded operator(s)
- Category Latest Changes
- Started by Tim_van_Beek
- Comments 4
- Last comment by zskoda
- Last Active Apr 19th 2010

I made a first draft of a page about unbounded operators, the battle plan contains some basic definitions, explanation of some subtleties of domain issues and what it means to be affiliated to a von Neumann algebra. Right now, only the rigged Hilbert space page refers to it.

- Discussion Type
- discussion topiceom
- Category Latest Changes
- Started by zskoda
- Comments 9
- Last comment by Urs
- Last Active Apr 19th 2010

- Discussion Type
- discussion topicGray-categories
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Apr 19th 2010

I added some examples to Gray-category, including also a non-example which has fooled several people.

- Discussion Type
- discussion topicDivision algebras and supersymmetry II
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by zskoda
- Last Active Apr 16th 2010

The nCafé is currently haunted by a bug that prevents any comments from being posted. This should eventually go away, hopefully. For the time being I post my comment in reply to the entry Division Algebras and Supersymmetry II here:

Thanks, John and John for these results. This is very pleasing.

The 3-s rule implies that the Poincaré superalgebra has a nontrivial 3-cocycle when spacetime has dimension 3, 4, 6, or 10.

Similarly, the 4-s rule implies that the Poincaré superalgebra has a nontrivial 4-cocycle when spacetime has dimension 4, 5, 7, or 11.

Very nice! That's what one would have hoped for.

Can you maybe see aspects of what makes these cocycles special compared to other cocycles that the Poincaré super Lie algebra has? What other cocycles that involve the spinors are there? Maybe there are a bunch of generic cocycles and then some special ones that depend on the dimension?

Is there any indication from the math to which extent and are the first two steps in a longer sequence of sequences? I might expect another sequence and corresponding to the fivebrane and the ninebrane. In other words, what happens when you look at -matrices with values in a division algebra for values of larger than 2 and 4?

Here a general comment related to the

**short exact sequences**of higher Lie algebras that you mention:properly speaking what matters is that these sequences are -categorical exact, namely are fibration sequences/fiber sequences in an -category of -algebras.

The cocycle itself is a morphism of -algebras

and the extension it classifies is the homotopy fiber of this

Forming in turn the homotopy fiber of that extension yields the loop space object of and thereby the fibration sequence

The fact that using the evident representatives of the equivalence classes of these objects the first three terms here also form an exact sequence of chain complexes is conceptually really a coicidence of little intrinsic meaning.

One way to demonstrate that we really have an -exact sequence here is to declare that the -category of -algebras is that presented by the standard modelstructure on dg-algebras on . In there we can show that is homotopy exact by observing that this is

*almost*a fibrant diagram, in that the second morphism is a fibration, the first object is fibrant and the other two objects are almost fibrant: their Chevalley-Eilenberg algebras are almost Sullivan algebras in that they are quasi-free. The only failure of fibrancy is that they don't obey the filtration property. But one can pass to a weakly equivalent fibrant replacement for and do the analog for without really changing the nature of the problem, given how simple is. Then we see that the sequence is indeed also homotopy-exact.This kind of discussion may not be relevant for the purposes of your article, but it does become relevant when one starts doing for instance higher gauge theory with these objects.

Here some further trivial comments on the article:

Might it be a good idea to mention the name "Fierz" somewhere?

page 3, below the first displayed math: The superstring Lie 2-superalgebra is [an] extension of

p. 4: the bracket of spinors defines [a] Lie superalgebra structure

p. 6, almost last line: this [is] equivalent to the fact

p. 13 this spinor identity also play[s] an important role in

p. 14: recall this [is] the component of the vector

- Discussion Type
- discussion topiclocally presentable category
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Apr 15th 2010

I tried at locally presentable category to incorporate the upshot of the query box discussions into the text, then moved the query boxes to the bottom

- Discussion Type
- discussion topicregular cardinal
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Apr 15th 2010

I gave regular cardinal its own page.

Because I am envisioning readers who know the basic concept of a cardinal, but might forget what “regular” means when they learn, say, about locally representable category. Formerly the Lab would just have pointed them to a long entry cardinal on cardinals in general, where the one-line definition they would be looking for was hidden somewhere. Now instead the link goes to a page where the definition is the first sentence.

Looks better to me, but let me know what you think.

- Discussion Type
- discussion topic(oo,1)-category of (oo,1)-presheaves
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Apr 15th 2010

added to (infinity,1)-category of (infinity,1)-presheaves a section on how it is the free (oo,1)-cocompletion

- Discussion Type
- discussion topic(oo,1)-category of (oo,1)-functors
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 15th 2010

added statement to (infinity,1)-category of (infinity,1)-functors on how limits and colimits are computed objectwise - here.

- Discussion Type
- discussion topiccoherence theorems
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Todd_Trimble
- Last Active Apr 15th 2010

- As further outgrowth spurred by Sridhar's work on anafunctors and cliques: a stubby start on coherence theorems.

- Discussion Type
- discussion topicCombinatorial model categories have presentations
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Apr 14th 2010

created reference-entry Combinatorial model categories have presentations on Dugger’s theorem

- Discussion Type
- discussion topicsmall set
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Apr 14th 2010

created small set

- Discussion Type
- discussion topicCategorified Symmetries
- Category Latest Changes
- Started by zskoda
- Comments 16
- Last comment by zskoda
- Last Active Apr 14th 2010

- Why I can not have this

1. Introduction 3

1.1 Categories and generalizations . . . . . . . . . . . . . . . . . 3

1.2. Basic idea of descent . . . . . . . . . . . . . . . . . . . . . . 5

2. From noncommutative spaces to categories 5

2.1. Idea of space and of noncommutative space . . . . . . . . . 5

2.2. Gel’fand-Naimark . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3. Nonaffine schemes and gluing of quasicoherent sheaves . . . 6

2.4. Noncommutative generalizations of QcohX . . . . . . . . . . 6

2.5. Abelian versus 1-categories . . . . . . . . . . . . . . . . . . 7

but instead I have automatic numbers like 1,2,3, 5, 8 (I know why, but how to avoid it??). I do NOT want nlab to make it like word, I want my numbering to stay it is, and if possible keeping the paragraphs. Putting > for quotation did not help!

- Discussion Type
- discussion topiclocalization of an (oo,1)-category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 14th 2010

edited localization of an (infinity,1)-category a bit. But more needs to be done.

- Discussion Type
- discussion topiclocally small (oo,1)-category
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Apr 14th 2010

- Discussion Type
- discussion topicclosed time-like curves
- Category Latest Changes
- Started by Ian_Durham
- Comments 46
- Last comment by zskoda
- Last Active Apr 12th 2010

- Added an entry on closed time-like curves. Also edited a few things in physicscontents in order to clean it up a bit.

- Discussion Type
- discussion topicmainstream mathematics
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active Apr 11th 2010

I have created in my own nlab, a programmatic entry mainstream mathematics (zoranskoda).

- Discussion Type
- discussion topicLie algebroid theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Apr 10th 2010

in reply to discussion on the blog I

added more details to Lie algebroid

added a reference by Courant to Lie algebroid, Poisson Lie algebroid and tangent Lie algebroid

created Legendre transformation as a placeholder that currently just serves to keep some references on Legendre transformation from the point of view of Lie algebroid theory.