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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory 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 differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck 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 homology homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories newpage 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-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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- Discussion Type
- discussion topic$$(n,n+1)$$-categories
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Urs
- Last Active Oct 20th 2009

I mentioned these at higher category theory and (n,n)-category, where it had been implied that the latter were as far as one could go in increasing the second parameter.

- Discussion Type
- discussion topicmatrix mechanics
- Category Latest Changes
- Started by David_Corfield
- Comments 10
- Last comment by David_Corfield
- Last Active Oct 20th 2009

- Began entry with that name.

- Discussion Type
- discussion topicringoid
- Category Latest Changes
- Started by Mike Shulman
- Comments 5
- Last comment by TobyBartels
- Last Active Oct 20th 2009

I think Ab-enriched category is a better name for the page than ringoid.

- Discussion Type
- discussion topic[[Jason Dusek]] joined and inspired me to start [[2-rig]].
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 20th 2009

Jason Dusek joined and inspired me to start 2-rig.

- Discussion Type
- discussion topicNew entry: [[poincare group]]
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by TobyBartels
- Last Active Oct 20th 2009

I wrote Poincare group as an entree to the project of carrying on in nLab the blog discussion on unitary representations of the Poincare group. I'm not a specialist of course, so I ask the experts to please examine for accuracy.

- Discussion Type
- discussion topicWrote [[short map]] and expanded [[isometry]]. (n/t)
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 20th 2009

- Discussion Type
- discussion topicG-principal oo-bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 19th 2009

I expanded and polished the discussion of the abstract definition of of G-principal oo-bundles in an arbitrary (oo,1)-topos at principal infinity-bundle.

Parts of this could/should eventually be moved/copied to action and action groupoid, but I won't do that now.

I'd be interested in comments. One would expect that for the case that the ambient (oo,1)-topos is Top this style of definition should be well known in the literature, but I am not sure if it is. In fact, the examples listed further below in the entry, (the construction by Quillen and the Stasheff-Wirth construction) seems to indicate that this very simple very general nonsense picture has not been conceived as such before. Could that be true?

- Discussion Type
- discussion topicRequest for Help
- Category Latest Changes
- Started by Andrew Stacey
- Comments 1
- Last comment by Andrew Stacey
- Last Active Oct 19th 2009

I've removed the request for help link from the main contents. It didn't get used much (though I got answers to my questions there!). Since we have yet to actually delete a page, rather than just blank the request for help page I've put a pointer to where one can ask questions (pretty similar to that on the FAQ).

- Discussion Type
- discussion topic[[two-valued topos]]
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by Mike Shulman
- Last Active Oct 19th 2009

I wrote two-valued topos to help me tighten up Mike's latest edit to cocomplete well-pointed topos.

- Discussion Type
- discussion topicReply to Roger Witte at [[foundations]]. (n/t)
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Oct 18th 2009

Reply to Roger Witte at foundations.

- Discussion Type
- discussion topicSch/S and S-Sch (notational point)
- Category Latest Changes
- Started by amathew
- Comments 3
- Last comment by zskoda
- Last Active Oct 18th 2009

I created a page for S-Sch as a notation for S-schemes to refer to in another post. Zoran pointed out that the notation is nonstandard (I do not know why I thought it was normal) and changed the title to [[Sch/S]]. I thus changed the first sentence to read Sch/S instead.

- Discussion Type
- discussion topicMinor changes (Hecke algebra, Hilbert basis theorem, additive envelope, etc.)
- Category Latest Changes
- Started by amathew
- Comments 4
- Last comment by JonAwbrey
- Last Active Oct 17th 2009

- I added a description of the degenerate affine Hecke algebra to the Hecke algebra page as one of the many variants.

I added the categorical generalization of Schur's lemma to that page.

I wrote a short stub on the additive envelope of a category, which Mike Shulman has expanded.

I mentioned the generalization of the Morse lemma to Hilbert manifolds.

I added the generalization of Hilbert's basis theorem to the case of where the ground ring is noetherian (not necessarily a field).

I wrote a short page on the Eilenberg swindle.

- Discussion Type
- discussion topicAkil Mathew
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Todd_Trimble
- Last Active Oct 17th 2009

I see that Akil Mathew has worked on a bunch of entries. Great! We should try to contact him and ask hom to record his changes here.

- Discussion Type
- discussion topicA-oo category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 17th 2009

Expanded the "Idea" section at A-infinity category.

- Discussion Type
- discussion topiccup product
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 17th 2009

Expanmded the idea section at cup product

- Discussion Type
- discussion topic[[Hugh Thomas]] joined to edit [[quiver]] (n/t)
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by Urs
- Last Active Oct 16th 2009

Hugh Thomas joined to edit quiver

- Discussion Type
- discussion topicthis and that
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 16th 2009

I added Alex's recent lecture notes to cobordism hypothesis and in that process polished some typesetting there slightly.

Then I was pleased to note that Noah Snyder joined us and worked on fusion category. I created a page for him.

- Discussion Type
- discussion topiccocomplete well-pointed topos
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by TobyBartels
- Last Active Oct 15th 2009

Wrote a proof at cocomplete well-pointed topos that characterizes Grothendieck universes and Set.

- Discussion Type
- discussion topicessential image
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Oct 15th 2009

I don't think that the (non-full) essential image of an arbitrary functor is well-defined.

- Discussion Type
- discussion topicfivebrane 6-group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 15th 2009

created fivebrane 6-group with the idea

- Discussion Type
- discussion topicexamples for smooth toposes
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 15th 2009

I added a fairly long (but still immensely incomplete) examples section to smooth topos.

I mention the "well adapted models" and say a few words about the point of it. Then I have a sectoin on how and in which sense algebraic geometry over a field takes place in a smooth topos. here the model is described easily, but I spend some lines on how to think of this. In the last example sections I have some remarks on non-preservation of limits in included subcategories of tame objects, but all that deserves further expansion of course.

- Discussion Type
- discussion topiceffects of foundations on "real" mathematics
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by JonAwbrey
- Last Active Oct 15th 2009

created effects of foundations on "real" mathematics and linked to it from foundations.

This is to archive an exchange between Toby and James on the blog here. The hope would be that eventually the list of examples is expanded here.

- Discussion Type
- discussion topicsmooth topos database
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 15th 2009

started filling in material into the planned database of smooth toposes at Models for Smooth Infinitesimal Analysis.

- Discussion Type
- discussion topicorthogonal group... in a lined topos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 15th 2009

I continued working my way through the lower realms of the Whitehead tower of the orthogonal group by creating special orthogonal group and, yes, orthogonal group.

For the time being the material present there just keeps repeating the Whitehead-tower story.

But I want more there, eventually: I have a query box at orthogonal group. The most general sensible-nonsense context to talk about the orthogonal group should be any lined topos.

I am wondering if there is anything interesting to be said, from that perspective. Incidentally, I was prepared in this context to also have to create general linear group, only to find to my pleasant surprise that Zoran had already created that some time back. And in fact, Zoran discusses there an algebro-geometric perspective on GL(n) which, I think, is actually usefully thought of as the perspective of GL(n) in the lined topos of, at least, presheaves on .

Presently I feel that I want eventually a discussion of all those seemingly boring old friends such as and and etc. in lined toposes and smooth toposes. Inspired not the least by the wealth of cool structure that even just carries in cases such as the -topos in Models for Smooth Infinitesimal Analysis.

- Discussion Type
- discussion topicFivebrane group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 14th 2009

created Fivebrane group but was being lazy:

essentially copy-and-pasted the intro from String group and then left a link to Fivebrane structure.

Then I went through String structure and Fivebrane structure and added links to String group and Fivebrane group.

- Discussion Type
- discussion topicHaynes Miller
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 14th 2009

created a page for Haynes Miller, since I just mentioned his name at string group as the one who coined that term.

not much on the page so far. Curiously, I found only a German Wikipedia page for him

- Discussion Type
- discussion topiciTeX - LaTeX differences in the FAQ
- Category Latest Changes
- Started by Andrew Stacey
- Comments 1
- Last comment by Andrew Stacey
- Last Active Oct 14th 2009

I've started listing differences between iTeX and LaTeX in the FAQ. That seemed the most logical place (I don't think we want a proliferation of places where users should look to find simple information) so either here or the HowTo seemed best. I chose the FAQ because the most likely time someone is going to look for this is when they notice something didn't look right.

The issue is that whilst iTeX is meant to be close to LaTeX they are

**never**going to be the same so it's worth listing known differences with their work-arounds.So far I've noted operator names, whitespace in

`\text`

, and some oddities on number handling.

- Discussion Type
- discussion topichomotopy group (of an oo-stack)
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 13th 2009

created homotopy group (of an infinity-stack)

a bit rough for the time being.

Also added a suitable link and short remark at homotopy group.

- Discussion Type
- discussion topicVishal Lama
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 13th 2009

Vishal Lama joined the Lab!

on his page he promises to create Lab pages on some books on category theory and topos theory. Great, I am looking forward to it

- Discussion Type
- discussion topicpath-structured smoth (oo,1)-toposes
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Oct 13th 2009

started working on

schreiber:path-structured (infinity,1)-toposes

This is a kind of survey of some constructions I've recently been spamming the nLab with.