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 accessible adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-geometry digraphs duality education elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity group-theory 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 infinity integration-theory k-theory kan lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology newpage nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory 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 subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal

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 topicfinite ∞-group
- Category Latest Changes
- Started by David_Corfield
- Comments 7
- Last comment by David_Corfield
- Last Active 11 hours ago

I started finite ∞-group, and added that same reference to Sylow p-subgroup.

- Discussion Type
- discussion topicKuiper's theorem
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by DavidRoberts
- Last Active 14 hours ago

following a suggestion by Zoran, I have created a stub (nothing more) for Kuiper’s theorem

- Discussion Type
- discussion topicidempotent complete (infinity,1)-category
- Category Latest Changes
- Started by Mike Shulman
- Comments 9
- Last comment by Mike Shulman
- Last Active 15 hours ago

At first Zoran's reply to my query at structured (infinity,1)-topos sounded as though he were saying "being idempotent-complete" were a structure on an (oo,1)-category rather than just a property of it. That had me worried for a while. It looks, though, like what he meant is that "being idempotent" is structure rather than a property, and that makes perfect sense. So I created idempotent complete (infinity,1)-category.

- Discussion Type
- discussion topicstack
- Category Latest Changes
- Started by zskoda
- Comments 9
- Last comment by zskoda
- Last Active 1 day ago

Stack entry says: "The notion of stack is the one-step vertical categorification of a sheaf." In Grothendieck's main works, like pursuing stacks and in the following works of French schools, stack is any-times categorification of a sheaf, and the one-step case is called more specifically 1-stack. We can talk thus about stack in narrow sense or 1-stacks and stacks in wider sense as n-stacks for all n. Topos literature mainly means that the stack is the same as internal 1-stack.

- Discussion Type
- discussion topicdescent
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by zskoda
- Last Active 1 day ago

I made some very minor changes to the introduction at descent. I hesitate to do more but at present the discussion does not seem that readable to me. Can someone look at it to see what they think? The intro seems to plunge in deep very quickly and so the ‘idea’ of descent as that of gluing local information together, does not come across to me. The article is lso quite long and perhaps needs splitting up a bit.

- Discussion Type
- discussion topicunivalence
- Category Latest Changes
- Started by Urs
- Comments 87
- Last comment by Mike Shulman
- Last Active 1 day ago

created univalence axiom

- Discussion Type
- discussion topic[[distribution]]
- Category Latest Changes
- Started by Todd_Trimble
- Comments 30
- Last comment by Mike Shulman
- Last Active 1 day ago

After sitting on this for days and hardly doing a thing, I added some applications to distribution and added a bit to the section on synthetic differential geometry. While I was dawdling, Andrew Stacey stepped in and added to some parts that needed expert attention -- thanks, Andrew.

- Discussion Type
- discussion topicSchwartz space
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Andrew Stacey
- Last Active 2 days ago

I have started to add some of the basic definitions and facts to

*Schwartz space*,*tempered distribution*and*Fourier transform of distributions*.Notice that we had an entry titled “Schwartz space” already since May 2013 (rev 1 by Andrew Stacey) which considered not spaces of smooth functions with rapidly decreasing derivatives, but locally convex TVSs $E$ “with the property that whenever $U$ is an absolutely convex neighbourhood of $0$ then it contains another, say $V$, such that $U$ maps to a precompact set in the normed vector space $E_V$.”

I had not been aware of this use of “Schwartz space” before, and Andrew gave neither reference nor discussion of the evident question, whether “the” Schwartz space is “a” Schwartz space. In June 2015 somebody saw our entry and shared his confusion about this point on Maths.SE here, with no reply so far.

I see that this other use of “Schwartz space” appears in Terzioglu 69 (web) where it is attributed to Grothendieck.

- Discussion Type
- discussion topicdinatural vs extranatural
- Category Latest Changes
- Started by Mike Shulman
- Comments 10
- Last comment by Yaron
- Last Active 2 days ago

Created extranatural transformation by moving the relevant information from dinatural transformation and adding the definition. Disagreements are welcome, but I feel that since dinaturals that aren't extranatural are so rare and harder to deal with and understand, extranaturals merit their own page.

- Discussion Type
- discussion topicdistribution of subspaces
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active 2 days ago

New entry distribution of subspaces and a disambiguating remark at distribution.

- Discussion Type
- discussion topicquantum electrodynamics
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active 2 days ago

I have been adding some more (historical) references to the entry

*quantum electrodynamics*(also at*quantum field theory*,*S-matrix*and*causal propagator*)

- Discussion Type
- discussion topiccausal perturbation theory
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by DavidRoberts
- Last Active 2 days ago

have been writing some Idea-section at

*causal perturbation theory*(currently this has much overlap with

*locally covariant perturbative quantum field theory*, eventially the latter will contain more stuff)

- Discussion Type
- discussion topicdescent object
- Category Latest Changes
- Started by FinnLawler
- Comments 15
- Last comment by Mike Shulman
- Last Active 3 days ago

Stephan Alexander Spahn has created descent object, with some definitions from Street’s

*Categorical and combinatorial aspects of descent theory*.If I get the opportunity this weekend I’ll add details from Street’s

*Correction to ’Fibrations in bicategories’*and Lack’s*Codescent objects and coherence*. Anyone know of any other references?Looking at Street’s paper again, what he describes as the ’$n=0$’ case of codescent objects looks to be just the notion of a coequalizer. I would have expected reflexive coequalizers, though, because the higher-$n$ case uses $n+2$-truncated simplicial objects. Is there a reason for this?

- Discussion Type
- discussion topicpasting scheme
- Category Latest Changes
- Started by Peter Heinig
- Comments 65
- Last comment by Harry Gindi
- Last Active 5 days ago

[New thread because, although it existed since 2012, pasting scheme appears not to have had a LatestChanges thread]

Started to expand pasting schemes. Intend to do more on this soon, in an integrated fashion with digraph and planar graph.

PLEASE note: ACCIDENTALLY a page pasting schemes was created too, as a result of some arcane issues with pluralized names of pages-still-empty. Please delete pasting schemes.

- Discussion Type
- discussion topicpullback of a distribution
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 5 days ago

created

*pullback of a distribution*, just for completeness

- Discussion Type
- discussion topicextension of distributions
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 5 days ago

have created

*extension of distributions*with the statement of the characterization of the space of*point-extensions*of distributions of finite degree of divergence: hereThis space is what gets identified as the space of renormalization freedom (counter-terms) in the formalization of perturbative renormalization of QFT in the approach of “causal perturbation theory”. Accordingly, the references for the theorem, as far as I am aware, are from the mathematical physics literature, going back to Epstein-Glaser 73. But the statement as such stands independently of its application to QFT, is fairly elementary and clearly of interest in itself. If anyone knows reference in the pure mathematics literature (earlier or independent or with more general statements that easily reduce to this one), please let me know.

- Discussion Type
- discussion topicWhitney extension theorem
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 5 days ago

brief note on

*Whitney extension theorem*

- Discussion Type
- discussion topicMackey functor
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Marc Hoyois
- Last Active 6 days ago

added an Idea-section to

*Mackey functor*(which used to be just a list of references). Also added more references.

- Discussion Type
- discussion topicalmost Kähler geometric quantization
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

created a stub for

*almost Kähler geometric quantization*, for the moment just so as to collect some pointers.

- Discussion Type
- discussion topicpseudoholomorphic vector bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

created a stub for

*pseudoholomorphic vector bundle*, for the moment just to record references

- Discussion Type
- discussion topicprojective space
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 7 days ago

started a stub for projective space

- Discussion Type
- discussion topicS-matrix
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Aug 8th 2017

added to

*S-matrix*a useful historical comment by Ron Maimon (see there for citation)

- Discussion Type
- discussion topicproduct of distributions
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 7th 2017

I gave

*product of distributions*its own entry. For the moment it just points to the definition in Hörmander’s book.This should eventually supercede the section “Multiplication of distributions” at

*distributions*, which I find suboptimal: that section starts very vaguely referring to physics as if the issue only appears there, and it keeps being very vague, with its three sub-subsections being little more than a pointer to one reference by Colombeau.I suggest to

remove that whole subsection at

*distribution*and leave just a pointer to*product of distributions*move the mentioning of Colombeau’s reference to

*product of distributions*and say how it relates to Hörmander’s definitionremove all vague mentioning of application in physics and instead add a pointer to

*Wick algebra*and*microcausal functional*, which I will create shortly.

- Discussion Type
- discussion topictensor product of distributions
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 7th 2017

created a minimum at

*tensor product of distributions*

- Discussion Type
- discussion topicinteraction picture
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 7th 2017

I have given

*interaction picture*genuine content (the entry used to be effectively empty):gave it one section “In quantum mechanics” with the standard kind of material going from interacting Hamiltonians to the definition of the S-matrix, and then a section “In quantum field theory” with an outline of which steps in the previous discussion require special technical care and how.

In the process I expanded the entry

*Dyson formula*. (In the end I effectively rewrote it, but now with a little broader perspective and more pointers).

- Discussion Type
- discussion topicBeck-Chevalley condition
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by David_Corfield
- Last Active Aug 7th 2017

at

*Beck-Chevalley condition*I have added an Examples-section*Pullbacks of opfibrations*with statement and proof that the diagram of presheaves induced by a pullback of a small obfibration satisfies Beck-Chevalley.

- Discussion Type
- discussion topicColombeau algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 7th 2017

at

*distribution*there used to be a mentioning of “Colombeau algebras”. I have now removed that paragraph there, and have given it its stand-alone stub entry*Colombeau algebra*, expanding it slightly.An expert might want to check. I haven’t actually looked into Colombeau algebras beyond a scanning of a review, and presently I don’t plan to delve into the topic. In fact their idea looks misguided to me.

All I mean to do here is to clean up the structure of the entry

*distribution*(see also my comments in the thread on products of distibutions, here) while preserving what others had written before.

- Discussion Type
- discussion topicaction
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Mike Shulman
- Last Active Aug 7th 2017

the page

*action*is also a mess. I have added a pointer to the somewhat more comprehensive module and am hereby moving the following discussion box from there to here:

[ begin forwarded discussion ]

+–{.query} I am wondering if we will need the notion of action which works in categories with product, i.e. $G\times X\to X$ and so on. There is also an action of one Lie algebra on another (for instance in some definitions of crossed module of Lie algebra, where $Aut$ is replaced by the Lie algebra of derivations. (a similar situation would seem to exist in various other categories where action is needed in a slightly wider context. I think most would be covered by an enriched setting but I am not sure.) Thoughts please.Tim

Yes, I think certainly all those types of action should eventually be described somewhere, possibly on this page. -Mike

Tim: I have added some of this above. There should be mention of actions of a monoid in a monoidal category on other objects, perhaps.

Mac Lane, VII.4, only requires a monoidal category to define actions. – Uday =–

[ end forwarded discussion ]

- Discussion Type
- discussion topicadiabatic switching
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 7th 2017

created

*adiabatic switching*(in quantum field theory) with a survey of the idea and references.

- Discussion Type
- discussion topicpoint-supported distribution
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 6th 2017

created

*point-supported distribution*