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- 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

- Discussion Type
- discussion topicalgebra
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active May 6th 2010

the topic-cluster “algebra” is stiil a little orphaned on the Lab, I find. I added a bit to

but these entries are still a bit pitiful. Maybe somebody feels challenged to turn them into good entries. Especially the latter.

Should we have pages algebra over a Lawvere theory, algebra over a PROP, etc? Some entries look like they want such links (for instance algebra itself).

- Discussion Type
- discussion topictrig & pi
- Category Latest Changes
- Started by Michael Hardy
- Comments 7
- Last comment by Urs
- Last Active May 6th 2010

- trigonometric identities and the irrationality of pi

I created this new page. I'm new here and I have no idea whether this sort of thing belongs in a place like this.

-- naively.....

- Discussion Type
- discussion topicobject
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 6th 2010

expanded object

- Discussion Type
- discussion topicnew and revised pages on logic stuff
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Mike Shulman
- Last Active May 6th 2010

- Recently have been adding to or creating various pages like essentially algebraic theory, Lawvere theory, Horn theory, signature, theory, and there may be others.

- Discussion Type
- discussion topicEilenberg-Zilber theorem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 5th 2010

added the cosimplicial version of the statement to Eilenberg-Zilber theorem and included a reference that gives a proof

- Discussion Type
- discussion topicClosed functors
- Category Latest Changes
- Started by TobyBartels
- Comments 18
- Last comment by Urs
- Last Active May 4th 2010

Eric wanted to know about closed functors, so we started a page. Probably somebody has written about these before, so references would be nice, if anybody knows them. (Google gives some hits that look promising, but I can’t read them now.)

- Discussion Type
- discussion topicHousekeeping at Frolicher spaces
- Category Latest Changes
- Started by Andrew Stacey
- Comments 1
- Last comment by Andrew Stacey
- Last Active May 4th 2010

I’ve done a bit of housekeeping at Froelicher space. I’ve split the page into pieces, putting each major section into its own section.

(This will necessitate a little reference chasing at manifolds of mapping spaces, and I need to put in some redirects)

I’ve put in a definition of curvaceous compactness at topological notions of Frölicher spaces. It works, but I’m not sure if it’s the right one yet.

- Discussion Type
- discussion topicenriched category theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 4th 2010

I edited the entry enriched category theory a bit, in an attempt to eventually bring that into decent shape.

I think we should eventually expand the list of related entries there and make it a floating toc.

- Discussion Type
- discussion topicexponential law
- Category Latest Changes
- Started by zskoda
- Comments 8
- Last comment by Mike Shulman
- Last Active May 4th 2010

It seems to me that despite so lenghty discussions and entry related to the mapping space-hm adjunction, only the ideal situations are treated (convenient categories of spaces). For this reason, I have created a new entry exponential law for spaces containing the conditions usually used in the category of ALL topological spaces, as well as few remarks about the pointed spaces.

- Discussion Type
- discussion topiccircle bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 3rd 2010

created stub for circle bundle

- Discussion Type
- discussion topiccircle group
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Andrew Stacey
- Last Active May 3rd 2010

proudly presenting the circle group ;-)

- Discussion Type
- discussion topicconcrete site
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 3rd 2010

created concrete site

- Discussion Type
- discussion topicgeneralized kernels
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by Mike Shulman
- Last Active May 3rd 2010

Created generalized kernel, with links from a lot of places.

- Discussion Type
- discussion topicsmooth (oo,1)-algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 2nd 2010

split off smooth (infinity,1)-algebra from derived smooth manifold and (infinity,1)-algebraic theory

- Discussion Type
- discussion topicCartesian fibration
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 2nd 2010

added more theorems to Cartesian fibration and polished the intro slightly

- Discussion Type
- discussion topiccategorification and groupoidification
- Category Latest Changes
- Started by bwebster
- Comments 10
- Last comment by bwebster
- Last Active May 2nd 2010

Taking the advice that if I write something on the internet, it should be stuck on the n-Lab, I've converted my recent comments in the n-category cafe and some old blog posts into a new page on the relationship between categorification and groupoidification: categorification via groupoid schemes

- Discussion Type
- discussion topicmanifolds of mapping spaces
- Category Latest Changes
- Started by Andrew Stacey
- Comments 21
- Last comment by Eric
- Last Active May 1st 2010

Split off the mapping spaces stuff from local addition into manifolds of mapping spaces. Still plenty to do and things to check (particularly on the linear stuff, and particularly figuring out what “compact” means). Haven’t actually deleted the relevant bit from local addition yet. Also, haven’t put a table of contents at manifolds of mapping spaces since I’ve learnt that the best way to get Urs to read something is to

*not*put a toc in.

- Discussion Type
- discussion topicsub-quasi-category
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Apr 29th 2010

created sub-quasi-category

- Discussion Type
- discussion topiccograph of a profunctor
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by Urs
- Last Active Apr 29th 2010

I created cograph of a profunctor and added some references to it at cograph of a functor. All the cograph pages could probably use some unifying work.

- Discussion Type
- discussion topicinner fibration
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 29th 2010

split off inner fibration from fibrations of quasi-categories and added remarks on how it models the (oo,1)-version of the notion of cograph of a profunctor

- Discussion Type
- discussion topicCasson invariant
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by DavidRoberts
- Last Active Apr 29th 2010

Casson invariant count SU(2) local systems of integral homology spheres. Thomas considered its holomorphic counterpart which is ultimately related to counting BPS states on Calabi-Yau 3-folds.

P.S. Hmm. Tags. New option. Great. Is there a list of tags ?