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 topicSimple groups
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active May 19th 2010

It got announced in another category, but here it is in Latest Changes:

Todd began (and then I edited) simple group.

- Discussion Type
- discussion topicconformal group
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 19th 2010

I wrote a quick entry conformal group, just from memory. Somebody could check and expand. In fact it would not be bad to have also a separate entry on conformal and on quasiconformal mappings.

- Discussion Type
- discussion topicchiral algebra
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 19th 2010

chiral algebra and improvements to vertex operator algebra

- Discussion Type
- discussion topicduplicate page compact operators
- Category Latest Changes
- Started by Tim_van_Beek
- Comments 8
- Last comment by zskoda
- Last Active May 18th 2010

somehow I missed that there already is a page compact operator and created compact operators. The plural is another error :-) the unsatisfied link that I used to create the page was “compact operators”. When I tried to rename it to the singular term it failed, of course. Now the page compact operators is simply superfluous, but as a non-administrator I cannot delete it…

- Discussion Type
- discussion topicsequential compactness
- Category Latest Changes
- Started by Andrew Stacey
- Comments 31
- Last comment by Andrew Stacey
- Last Active May 18th 2010

Created sequential compactness, should probably link to all these compactness variations from compact space. Not sure if I got the “iff” bit right in the relationship with compactness itself; will check it myself if no-one fixes it in the meantime.

I decided that this was the key property in manifolds of mapping spaces and to stop trying to figure out a Froelicher version of sequentially compact for the time-being.

- Discussion Type
- discussion topictwist
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active May 17th 2010

the term “twist” or “twisted” is one of those insanely ambiguous terms in math. Trying to follow our recent agreement on how to deal with ambiguous page names, I tried to indicate this at twist .

- Discussion Type
- discussion topicLax-idempotent monads
- Category Latest Changes
- Started by FinnLawler
- Comments 10
- Last comment by Mike Shulman
- Last Active May 17th 2010

Created lax-idempotent 2-monad, with some definitions from Kelly–Lack. I think Kock has a couple of others. I’ll add more, like proofs of the equivalence of the definitions, and more on the cocompletion example, later (next week, probably).

- Discussion Type
- discussion topicFinal version of thesis
- Category Latest Changes
- Started by DavidRoberts
- Comments 2
- Last comment by Harry Gindi
- Last Active May 17th 2010

The final copy of my thesis is up on the lab. Available from Fundamental Bigroupoids and 2-Covering Spaces. I’ve fixed the typo in definition 5.1 that made it into the print copy ;)

Thus I’ve updated the links at David Roberts, the above linked page, and on my private web home page. If anyone knows of any other places it is linked, please let me know, or update the link to point to DMRthesis_final.pdf, instead of DMR_thesis.pdf.

Now to all the other projects that are on the back burner, time permitting…

- Discussion Type
- discussion topicIntroductions to category theory in physics
- Category Latest Changes
- Started by Urs
- Comments 37
- Last comment by Ian_Durham
- Last Active May 17th 2010

started a section Introductions to category theory in physics at the woefully imperfect entry higher category theory and physics. So far this contains mostly th expository articles by Bob Coecke.

- Discussion Type
- discussion topiccategory with duals
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 16th 2010

I see that Peter Selinger edited and added material to category with duals

- Discussion Type
- discussion topic2-topos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 16th 2010

stub for 2-topos (mostly so that the links we have to it do point somewhere at least a little bit useful)

- Discussion Type
- discussion topicpresheaves and overcategories
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by DavidRoberts
- Last Active May 16th 2010

I put the theorem about presheaves on overcategories and overcategories of presheaves that had its own page at functors and comma categories into the Properties-section at category of presheaves: Presheaves on over-categories and over-categories of presheaves.

Then I added the analogous proposition for (oo,1)-presheaves at (∞,1)-category of (∞,1)-presheaves -- Interaction with overcategories

Incidentally, there is some bug on the nLab that might be related to the one Toby just pointed out in the thread on scrollboxes: Trying to put links to subsections of nLab entries into nLab entries is often troublesome. The Markup-code for links gets mixed up by the hash-sign, usually. Then usually the html-code will work. But at the moment at category of presheaves I cant get that to work either...

- Discussion Type
- discussion topicmonoidal categories sidebar
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by Urs
- Last Active May 16th 2010

Prompted by Peter Selinger’s recent email on the catlist, I created a floating TOC for monoidal categories, added it to a lot of pages, created a couple of stubs for ribbon category and pivotal category, and corrected the redirect for autonomous category to point to rigid monoidal category rather than compact closed category. We are still missing stubs for balanced monoidal category and traced monoidal category and dagger monoidal category – anyone want to fill them in?

- Discussion Type
- discussion topictoc for topos theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 14th 2010

started a floating toc for topos theory. See at the right of topos.

Please feel encouraged to expand and improve the structure.

- Discussion Type
- discussion topicgroupoid cardinality
- Category Latest Changes
- Started by Tim_Porter
- Comments 10
- Last comment by domenico_fiorenza
- Last Active May 14th 2010

- I have made a comment on the groupoid cardinality page. It draws peoples attention to Quinn's notes on TQFTs which uses a notion of homotopy order to construct scaling factors in a simple TQFT. This does not seem to be mentioned in stuff that I have seen and googling gets very few hits for this. It is clearly the same as groupoid cardinality when both are defined.

- Discussion Type
- discussion topic[functional]
- Category Latest Changes
- Started by DavidRoberts
- Comments 32
- Last comment by zskoda
- Last Active May 14th 2010

Added functional. A bit sketchy.

- Discussion Type
- discussion topic(oo,1)-sheaf
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 14th 2010

finally noticed that (infinity,1)-sheaf was hardly even a stub. Have now filled some genuine content in there.

- Discussion Type
- discussion topicfree monad
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active May 13th 2010

Created free monad with a discussion of some of the subtleties and the notion of “algebraically-free”.

- Discussion Type
- discussion topicdifferential topology of mapping spaces
- Category Latest Changes
- Started by Andrew Stacey
- Comments 28
- Last comment by Urs
- Last Active May 13th 2010

I’ve started porting my notes “differential topology of loop spaces” over to the nlab, starting at differential topology of mapping spaces. As part of the transfer, I intend to map out the theory for general mapping spaces, not just loop spaces (that’ll give me a bit more motivation to do the transfer since just cut-and-paste is boring!). I’ve just copied over the contents and the introduction so far and haven’t edited them as yet. In particular, although I’ve wikilinked all the original section names, these will get changed as they currently focus on loop spaces.

The introduction to the original document ended as follows (not copied over to the new version):

This document began life as notes from talks given at NTNU and at Sheffield so I would like to thank the topologists at those institutions, and in particular Nils Baas, for letting me talk about my favourite mathematical subject. I would also like to thank Ralph Cohen and the “loop group” at Stanford.

This is by no means a ﬁnished document, as an example it is somewhat sparse on references. Any comments, suggestions, and constructive criticism will be welcomed.

The second paragraph is sort-of stating the obvious as it holds to some extent for any nLab page! And I would love to be able to add some more names to the list in the first paragraph. Again, I hope it goes without saying but I’ll say it anyway: although I anticipate being the main contributor to these pages, it is not

*my*project! I would love it if people read it, add comments, add other stuff, write (constructive) graffiti, link it to other stuff.

- Discussion Type
- discussion topicmapping space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 13th 2010

Currently mapping space redirects to internal hom.

I have now at least added a link to Andrew’s recent manifold structure of mapping spaces to the list of examples there, but it wouldn’t hurt if someone wrote a bit more about mapping spaces in topology etc.

- Discussion Type
- discussion topiccover
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active May 12th 2010

The entry cover was in a pitiful state. I tried to brush it up a bit. But I am afraid I am still not doing it justice. But also I don’t quite have the leisure for a good exposition right now. What I really want is to create an entry good cover in a moment…

- Discussion Type
- discussion topicSullivan construction
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active May 12th 2010

stub for Sullivan construction (I got annoyed that the entry didn’t exist, but also don’t feel like doing it justice right now)

- Discussion Type
- discussion topicinfinitesimal object
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active May 11th 2010

added a section Spaces of infinitesimal simplices

- Discussion Type
- discussion topick-tuply monoidal n-category
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active May 11th 2010

Because I want to point to it in a reply to the current discussion on the Category Theory Mailing list, I tried to brush up the entry k-tuply monoidal n-category a bit.

In particular I

expanded the Idea section and added some statements that had been missing there;

reacted to the old query box discussion there and moved the query box to the very bottom;

added a section on k-tuply monoidal $\infty$-groupoids and $\infty$-stacks here.

added a section on k-tuply monoidal $(n,1)$-categories here

- Discussion Type
- discussion topicAT category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by Todd_Trimble
- Last Active May 11th 2010

I had started an article on AT category (which I originally mis-titled as “AT categories” – thank you Toby for fixing this!), but getting a little stuck here and there. I’m using the exchange between Freyd and Pratt on the categories mailing list (what else is there?) as my reference, but as is so often the case, Freyd’s discussion is a little too snappy and terse for me to follow it down to all the nitty-gritty details.

There’s a minor point I’m having trouble verifying: that coproducts are disjoint (as a consequence of the AT axioms that Freyd had enunciated thus far where he made that claim, in his main post), particularly that the coprojections are monic. Presumably this isn’t too hard and I’m just being dense. A slightly less than minor point: I’m having trouble verifying Ab-enrichment of the category of type A objects. I believe Freyd as abelian-categories-guru implicitly – I don’t doubt him. Can anyone help?

- Discussion Type
- discussion topicinvariant polynomial
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 10th 2010

created invariant polynomial

- Discussion Type
- discussion topicinterval category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 9th 2010

polished a bit and expanded a bit at interval category (nothing deep, just so that it looks better)

- Discussion Type
- discussion topicNoncommutative geometry and stochastic calculus
- Category Latest Changes
- Started by Eric
- Comments 6
- Last comment by Todd_Trimble
- Last Active May 8th 2010

Todd is helping me understand opposite categories beginning with $FinSet^{op}$ here.

This discussion helped prompt some improvement of the page opposite category. When I look at that page now, I see the statement:

The idea of noncommutative geometry is essentially to define a category of

*spaces*as the opposite category of a category of algebras.This reminded me of a remark I made in the “Forward” to a paper I wrote back in 2002, so I’ve now itexified that “Foreward” here:

Noncommutative Geometry and Stochastic Calculus

By the way, this also suggests that the category $FinSet$ is the category of

*spaces*opposite to the category of finite Boolean algebras in the sense of space and quantity.

- Discussion Type
- discussion topicspinors in Yang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Tim_van_Beek
- Last Active May 7th 2010

I noticed that recently Konrad Waldorf created a very nice article

I went through it and added definition/theorem/proof-environments and lots of hyperlinks. Some of them are unsaturated. Maybe somebody feels inspired to create corresponding entries.

- Discussion Type
- discussion topicessential geometric morphism
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active May 7th 2010

started essential geometric morphism