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- Discussion Type
- discussion topicLie group cohomology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 4th 2010

split off Lie group cohomology from group cohomology

- Discussion Type
- discussion topicA composable pair is the stub of a commutative triangle.
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Sep 3rd 2010

Stubs at composable pair and commutative triangle

- Discussion Type
- discussion topicBaues-Wirsching cohomology
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Sep 3rd 2010

I have added a bit of history to the entry on Baues-Wirsching cohomology. Whilst looking for something else I found a paper by Charlie Wells from 1979, extending the earlier ideas of Leech cohomology for semigroups to small categories. He defines various types of extension and classifies them using the same methods as B and W used a few years later.

- Discussion Type
- discussion topicChern-Simons form
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Sep 3rd 2010

am starting curvature characteristic form and Chern-Simons form.

But still working…

- Discussion Type
- discussion topicmatrix Lie group / matrix Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Sep 2nd 2010

started one-line stubs for matrix Lie group and matrix Lie algebra just so that the links to these, which started appearing at parallel transport and elsewhere do point somewhere

- Discussion Type
- discussion topic[skeleton]
- Category Latest Changes
- Started by DavidRoberts
- Comments 6
- Last comment by TobyBartels
- Last Active Sep 2nd 2010

Added a bit to skeleton about skeletons of internal categories

- Discussion Type
- discussion topicsplit hypercover
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Aug 31st 2010

created split hypercover

- Discussion Type
- discussion topicexact functor
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 30th 2010

added to exact functor a new subsection “Between abelian categories” and listed there (briefly) the standard characterizations of left/right exact functors in terms of preservation of left/right exact sequences.

Also added a reference by Michael Barr on the relation between exactness and respect for homology in very general contexts.

- Discussion Type
- discussion topicinjective object
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Aug 27th 2010

added to injective object propositions and examples for injective modules and injective abelian groups

P.S. I am checking if I am missing something: Toën on page 48/49 here behaves as if it were clear that there is a model structure on positive cochain complexes of R-modules for all R in which the fibrations are the epis. But from the statements that i am aware of at model structure on chain complexes, in general the fibrations may be taken to be those epis that have injective kernels. For $R$ a field this is an empty condition and we are in business and find the familiar model structures. But for $R$ not a field? Notably simply $R = \mathbb{Z}$ What am I missing?

- Discussion Type
- discussion topicNew logic articles
- Category Latest Changes
- Started by TobyBartels
- Comments 6
- Last comment by Mike Shulman
- Last Active Aug 27th 2010

- Discussion Type
- discussion topic[over quasi-category]
- Category Latest Changes
- Started by Harry Gindi
- Comments 5
- Last comment by Harry Gindi
- Last Active Aug 26th 2010

I fixed the definition at over quasi-category so it makes the adjointness relationship clearer between overcategories and joins. In particular, Lurie’s notation and definition makes it very hard to see this. It’s much easier to see what’s going on when we look at things as follows: The join with $K$ fixed in the first coordinate, $S\mapsto i_K^{K\star S}: K\to K\star S$, where $i_K^{K\star S}$ is the canonical inclusion, is a functor $SSet\to (K\downarrow SSet)$. Then the undercategory construction gives the adjoint to this functor sending $(K\downarrow SSet) \to SSet$. This makes it substantially clearer to understand what’s going on, since $Hom_{SSet}(S, X_{F/}):= Hom_{K\downarrow SSet}(i_K^{K\star S}, F)$ is the set of those maps $f:K\star S\to X$ such that $f|K=f\circ i_K^{K\star S}=F$.

Lurie’s notation $Hom_{SSet}(S, X_{F/}):= Hom_F(K\star S, X)$ is nonstandard and inferior, since it obscures the obvious adjointness property.

The definition for overcategories is “dual” (by looking at the join of $K$ on the right).

- Discussion Type
- discussion topicnice simplicial topological space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 25th 2010

started nice simplicial topological space with material provided by David Roberts

- Discussion Type
- discussion topicsimplicial topological space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 24th 2010

stub for simplicial topological space

- Discussion Type
- discussion topicoo-Lie groupoid
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Aug 23rd 2010

considerably expanded Lie infinity-groupoid. But still stubby.

- Discussion Type
- discussion topicSomething about nothing
- Category Latest Changes
- Started by TobyBartels
- Comments 21
- Last comment by TobyBartels
- Last Active Aug 21st 2010

- Discussion Type
- discussion topicSifted colimits
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by TobyBartels
- Last Active Aug 20th 2010

Aleks Kissinger has given us sifted colimit. Although I don’t quite understand the definition.

- Discussion Type
- discussion topicSequential nets
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by TobyBartels
- Last Active Aug 20th 2010

I revisited some old discussion with Mike at sequence. Are you happy now, Mike?

- Discussion Type
- discussion topicmodel structure on cosimplicial abelian groups
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 19th 2010

wrote model structure on cosimplicial abelian groups with a detailed proof that it is a simplicial model category.

This statement must be very well known, but it seems it is good to give an explicit proof.

- Discussion Type
- discussion topicJointly epimorphic families
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by TobyBartels
- Last Active Aug 19th 2010

I linked to it, so here is jointly epimorphic family, our newest stub.

- Discussion Type
- discussion topicoo-vector bundles
- Category Latest Changes
- Started by Urs
- Comments 36
- Last comment by zskoda
- Last Active Aug 18th 2010

started oo-vector bundle on my personal web, following my latest remarks in the thread here on deformation theory.

- Discussion Type
- discussion topicindecomposable object
- Category Latest Changes
- Started by FinnLawler
- Comments 17
- Last comment by Marc
- Last Active Aug 18th 2010

New page: indecomposable object, following (what I think is) Johnstone's definition. I also found it in some online topos theory lecture notes by Ieke Moerdijk and Jaap van Oosten.

Lambek and Scott give a different definition in

*Intro. to Higher-order Cat. Log.*, p. 168. I'm not sure how it relates to Johnstone's.I've also given a proof that indecomposable <=> connected in an extensive category. I'd be interested to know whether this hypothesis is the weakest possible, if anyone has any ideas (or just likely-looking references).

- Discussion Type
- discussion topicThin categories
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Aug 18th 2010

I could have sworn that we had something for thin category, at least a redirect, but we don’t. Or didn’t. Now we do.

Not much to it, just a note of terminology, like inductive limit or (0,1)-topos.

There’s also a diagram that I can’t to get to work there, if anybody wants to help.

- Discussion Type
- discussion topiccircle n-bundle with connection
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 18th 2010

created circle n-bundle with connection.

See the nForum thread on oo-Chern Weil theory for background.

- Discussion Type
- discussion topicGleason's Theorem for POVMs
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by Ian_Durham
- Last Active Aug 18th 2010

This is mathematically much simpler than the classical Gleason’s Theorem, but I added it to Gleason’s theorem anyway.

- Discussion Type
- discussion topicgluing from localizations
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Aug 17th 2010

In gluing categories from localizations (zoranskoda) the main section

**From a family of localizations to a comonad**is fully rewritten in improved notation. In other way, it is explained better how to get a comonad from a cover of a category by not necessarily compatible flat localizations. This generalizes the Sweedler's coring to relative situations. Now from such data one can make a two category, which I will explain in few days.

This is a preliminary to something I am writing at the moment namely to explain in such terms actions of comonads and monoidal categories on such descent categories. This part will be analogous to description of equivariant maps among G-manifolds in pairs of local charts, but because of the distributive laws with coherences, the thing complicates.

- Discussion Type
- discussion topicstacked cover
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 17th 2010

started stacked cover

- Discussion Type
- discussion topicphenomenology
- Category Latest Changes
- Started by zskoda
- Comments 8
- Last comment by Todd_Trimble
- Last Active Aug 17th 2010

Last entry before lunch: phenomenology. Physics…

- Discussion Type
- discussion topicQuantification
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by TobyBartels
- Last Active Aug 17th 2010

I started quantifier, but I ran out of time to say all that I wanted. I’ll probably get back to it in a couple of hours.

- Discussion Type
- discussion topicContents
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Mike Shulman
- Last Active Aug 17th 2010

I redid everything that includes contents using the new click-based menu system. This includes HomePage; there didn’t seem to be a need anymore to have two columns, so I put them back in one column. However, those are separate issues; we could put them back in two columns again and still do the click thingy.

- Discussion Type
- discussion topicStates in statistical physics
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by Ian_Durham
- Last Active Aug 16th 2010

I added some stuff about states in statistical physics to state.