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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 complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor 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 itex k-theory lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics 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 science set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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- Discussion Type
- discussion topicorbifold K-theory
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jul 10th 2020

- Discussion Type
- discussion topictest topos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 10th 2020

Currently nothing but a pointer to page 16 of

- Denis-Charles Cisinski,
*Les préfaisceaux comme types d’homotopie|Les préfaisceaux comme modèles des types d’homotopie*, Astérisque, Volume 308, Soc. Math. France (2006), 392 pages (numdam:AST_2006__308__R1_0, pdf)

Just so as to sort out the issue with where the term appears, as discussed in another thread here.

- Denis-Charles Cisinski,

- Discussion Type
- discussion topicDenis-Charles Cisinski
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Jul 10th 2020

created website-link page Denis-Charles Cisinski

- Discussion Type
- discussion topiccanonical model structure
- Category Latest Changes
- Started by Richard Williamson
- Comments 1
- Last comment by Richard Williamson
- Last Active Jul 10th 2020

Linking to the page canonical model structure for 2-categories in a couple of places.

- Discussion Type
- discussion topicgeometric realization of simplicial topological spaces
- Category Latest Changes
- Started by Urs
- Comments 69
- Last comment by Urs
- Last Active Jul 10th 2020

started an entry geometric realization of simplicial topological spaces.

I decided this is a topic big enough to justify splitting it off from geometric realization (of simplicial sets).

But not much there yet. I just wanted to record for the moment that this realization too, does preserve pullbacks.

- Discussion Type
- discussion topiccanonical model structure on 2-categories
- Category Latest Changes
- Started by Richard Williamson
- Comments 1
- Last comment by Richard Williamson
- Last Active Jul 10th 2020

- Discussion Type
- discussion topicamplituhedron
- Category Latest Changes
- Started by zskoda
- Comments 34
- Last comment by Urs
- Last Active Jul 10th 2020

- Discussion Type
- discussion topicabstract elementary class
- Category Latest Changes
- Started by Mike Shulman
- Comments 5
- Last comment by zskoda
- Last Active Jul 9th 2020

- Discussion Type
- discussion topic(infinity,1)-category
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active Jul 9th 2020

I worked on brushing up (infinity,1)-category a little

mostly I added in a section on homotopical categories, using some paragraphs from Andre Joyal's message to the CatTheory mailing list.

in this context I also rearranged the order of the subsections

I removed in the introduction the link to the page "Why (oo,1)-categories" and instead expanded the Idea section a bit.

added a paragraph to the beginning of the subsection on model categories

added the new Dugger/Spivak references on the relation between quasi-cats and SSet-cats (added that also to quasi-category and to relation between quasi-categories and simplicial categories)

- Discussion Type
- discussion topicHans-Joachim Baues
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by zskoda
- Last Active Jul 9th 2020

- Discussion Type
- discussion topichomotopy theory
- Category Latest Changes
- Started by Tim_Porter
- Comments 18
- Last comment by Urs
- Last Active Jul 9th 2020

I have deleted an old out of date query box from homotopy theory.

- Discussion Type
- discussion topiccategory theory
- Category Latest Changes
- Started by Eric
- Comments 70
- Last comment by Urs
- Last Active Jul 9th 2020

I removed some spam on category theory.

- Discussion Type
- discussion topicAlexander Körschgen
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 9th 2020

- Discussion Type
- discussion topicBelle experiment
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 9th 2020

- Discussion Type
- discussion topictheory of categories
- Category Latest Changes
- Started by Thomas Holder
- Comments 2
- Last comment by Thomas Holder
- Last Active Jul 8th 2020

- Discussion Type
- discussion topicexceptional structures -- contents
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by David_Corfield
- Last Active Jul 8th 2020

- Discussion Type
- discussion topicfunctorial geometry
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by DavidRoberts
- Last Active Jul 7th 2020

The scan of the writeup of Grothendieck’s 73 Buffalo lecture that we point to at

*functorial geometry*is really badly done. Is there a better scan or any other re-typing available?

- Discussion Type
- discussion topicdependent linear type theory
- Category Latest Changes
- Started by Urs
- Comments 70
- Last comment by Mike Shulman
- Last Active Jul 7th 2020

Following discussion in some other threads, I thought one should make it explicit and so I created an entry

Currently this contains some (hopefully) evident remarks of what “dependent linear type theory” reasonably should be at least, namely a hyperdoctrine with values in linear type theories.

The entry keeps saying “should”. I’d ask readers to please either point to previous proposals for what “linear dependent type theory” is/should be, or criticise or else further expand/refine what hopefully are the obvious definitions.

This is hopefully uncontroversial and should be regarded an obvious triviality. But it seems it might be one of those hidden trivialities which deserve to be highlighted a bit more. I am getting the impression that there is a big story hiding here.

Thanks for whatever input you might have.

- Discussion Type
- discussion topiclax extranatural transformation
- Category Latest Changes
- Started by Théo de Oliveira S.
- Comments 1
- Last comment by Théo de Oliveira S.
- Last Active Jul 7th 2020

Started a page on lax extranatural transformations. I’ll add more material to here (very) slowly as needed for the page on lax biends.

- Discussion Type
- discussion topiclax biend
- Category Latest Changes
- Started by Théo de Oliveira S.
- Comments 1
- Last comment by Théo de Oliveira S.
- Last Active Jul 7th 2020

- Discussion Type
- discussion topicadjoint modality
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 7th 2020

added pointer to p. 245 of

$U X \;\colon\; \array{ comodal X &\longrightarrow& X &\longrightarrow& modal X \\ opposite\;1 && unity && opposite\;2 }$*Sets for Mathematics*for the idea of

- Discussion Type
- discussion topicSets for Mathematics
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 7th 2020

I gave

*Sets for Mathematics*a category:reference entry and linked to it from*ETCS*and from*set theory*, to start with.David Corfield kindly alerts me, which I had missed before, that appendix C.1 there has a clear statement of Lawvere’s proposal from 94 of how to think of categorical logic as formalizing objective and subjective logic (to which enty I have now added the relevant quotes).

- Discussion Type
- discussion topicCohesive Toposes and Cantor's "lauter Einsen"
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 7th 2020

- Discussion Type
- discussion topicmodel structure on simplicial presheaves
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Jul 7th 2020

fianlly added the details of Dugger’s description of cofibrant objects in the projective model structure on simplicial presheaves in the section Cofibrant objects.

- Discussion Type
- discussion topicspherical T-duality
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Jul 7th 2020

created a quick pointer to, with a brief remark on,

*spherical T-duality*

- Discussion Type
- discussion topiccellular homology
- Category Latest Changes
- Started by Todd_Trimble
- Comments 9
- Last comment by Urs
- Last Active Jul 6th 2020

I added to Tim’s stub on cellular homology. Still a bit rough around the edges perhaps. An example (say real projective space) would also be nice.

- Discussion Type
- discussion topicEvan Cavallo
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 6th 2020

brief

`category:people`

-entry for hyperlinking references at*generalized (Eilenberg-Steenrod) cohomology*

- Discussion Type
- discussion topicgeneralized (Eilenberg-Steenrod) cohomology
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jul 6th 2020

I have added the version of the axioms for reduced cohomology here at

*generalized (Eilenberg-Steenrod) cohomology*(and also at*reduced cohomology*), and I have further expanded and streamlined (I hope) the Idea-section.More harmonization (notation, conventions) is necessary in this and related entries. Later.

- Discussion Type
- discussion topicwalking 2-isomorphism with trivial boundary
- Category Latest Changes
- Started by Richard Williamson
- Comments 3
- Last comment by Richard Williamson
- Last Active Jul 6th 2020

Creating the page, which I intend to use at Lack fibration. If I have not made a mistake, this is a 2-groupoid model of the 2-truncation of the 2-sphere, and I have added remarks of this nature to the page, along with a ’computation’ of $\pi_{2}\left(S^{2}\right)$ using this model.

- Discussion Type
- discussion topicElephant
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Jul 6th 2020