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2-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology combinatorics complex-geometry computable-mathematics computer-science connection constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education 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 homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory lie lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories 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 type type-theory universal variational-calculus

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- Discussion Type
- discussion topicpariah group
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by DavidRoberts
- Last Active May 20th 2019

- Discussion Type
- discussion topicArchive of Formal Proofs
- Category Latest Changes
- Started by Daniel Luckhardt
- Comments 2
- Last comment by Urs
- Last Active May 20th 2019

- Discussion Type
- discussion topic(infinity,1)-category
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Urs
- Last Active May 20th 2019

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 topicAndrew Kresch
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 20th 2019

brief

`category:people`

-entry for hyperlinking references at*Deligne-Mumford stack*and*orbifold*

- Discussion Type
- discussion topicDeligne-Mumford stack
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 20th 2019

added this pointer:

- Andrew Kresch,
*On the geometry of Deligne-Mumford stacks*(doi:10.5167/uzh-21342, pdf), in D. Abramovich, A. Bertram, L. Katzarkov, R. Pandharipande, M. Thaddeus (eds.)*Algebraic Geometry: Seattle 2005*, Proceedings of Symposia in Pure Mathematics Providence, Rhode Island: American Mathematical Society, 259-271 (pspum-80-1)

Was looking for references to point readers to for background on the idea that DM-stacks and orbidfolds are essentially the same thing, realized in two different geometric categories (up to a list of inessential technical conditions). This is the best I have found so far. If anyone knows further references along these lines, please drop a note.

- Andrew Kresch,

- Discussion Type
- discussion topicFischer group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 20th 2019

stub, just for completeness of the Happy Family

- Discussion Type
- discussion topicsporadic finite simple group
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active May 20th 2019

- Discussion Type
- discussion topicConway group
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by David_Corfield
- Last Active May 20th 2019

- Discussion Type
- discussion topicuniversal exceptionalism
- Category Latest Changes
- Started by Urs
- Comments 69
- Last comment by Urs
- Last Active May 20th 2019

started

*universal exceptionalism*related discussion is taking place on g+ here

- Discussion Type
- discussion topicUniMath project
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 20th 2019

For completeness, so that we now have this list:

- Discussion Type
- discussion topicequivariant stable homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active May 19th 2019

I am slowly creating a bunch of entries on basic concepts of equivariant stable homotopy theory, such as

- equivariant suspension spectrum, equivariant sphere spectrum, equivariant homotopy groups, RO(G)-grading, fixed point spectrum, tom Dieck splitting

At the moment I am mostly just indexing Stefan Schwede’s

- Discussion Type
- discussion topicBorel equivariant cohomology
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 19th 2019

- Discussion Type
- discussion topicdifferentiable stack
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 19th 2019

I have added pdf-links to the reference

- David Carchedi,
*Categorical Properties of Topological and Diffentiable Stacks*, PhD thesis, Universiteit Utrecht, 2011 (dspace:1874/208971, pdf)

and promoted this to the top of the list, since I suppose this is the most comprehensive account that a reader might want to go to first. Will also edit accordingly at

*topological stack*- David Carchedi,

- Discussion Type
- discussion topicJohn Ratcliffe
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by DavidRoberts
- Last Active May 19th 2019

brief

`category:people`

-entry for hyperlinking references at*orbifold*and*hyperbolic manifold*, in particular to this excellent book:- John Ratcliffe,
*Foundations of Hyperbolic Manifolds*, Springer 2006 (doi:10.1007/978-0-387-47322-2, pdf)

- John Ratcliffe,

- Discussion Type
- discussion topicmultiverse
- Category Latest Changes
- Started by Urs
- Comments 35
- Last comment by Urs
- Last Active May 19th 2019

I kept being annoyed about the nature of discussion of the “multiverse” (the one in cosmology, not the one in set theory). Now I thought instead of steadily being annoyed, I should start an $n$Lab entry that does it better. So I did now (or tried to), at

*multiverse*.

- Discussion Type
- discussion topicYoneda lemma
- Category Latest Changes
- Started by Urs
- Comments 72
- Last comment by Mike Shulman
- Last Active May 19th 2019

Todd,

you added to Yoneda lemma the sentence

In brief, the principle is that the identity morphism $id_x: x \to x$ is the universal generalized element of $x$. This simple principle is surprisingly pervasive throughout category theory.

Maybe it would be good to expand on that. One might think that the universal property of a genralized element is that every other one factors through it uniquely. That this is true for the generalized element $id_x$ is a tautological statement that does not need or imply the Yoneda lemma, it seems.

- Discussion Type
- discussion topicNico Courts
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active May 18th 2019

- Discussion Type
- discussion topicJames Liu
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 18th 2019

- Discussion Type
- discussion topicduality between heterotic and type II string theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 18th 2019

- Discussion Type
- discussion topicstring-string duality
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 18th 2019

- Discussion Type
- discussion topicRamzi Khuri
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 18th 2019

- Discussion Type
- discussion topicstring coupling constant
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 18th 2019

- Discussion Type
- discussion topicRoberto Volpato
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 18th 2019

brief

`category:people`

-entry for hyperlinking references at*moonshine*,*duality between heterotic and type II string theory*,*Riemannian orbifold*and maybe elsewhere

- Discussion Type
- discussion topicallegory
- Category Latest Changes
- Started by Todd_Trimble
- Comments 40
- Last comment by Daniel Luckhardt
- Last Active May 18th 2019

Added some examples to allegory, including that of modular lattice as one-object allegory.

- Discussion Type
- discussion topic2-spectral triple
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active May 18th 2019

added more references to 2-spectral triple (as far as I can see Jürg Fröhlich with his students was the first to try to formalize this to some extent)

- Discussion Type
- discussion topicfolklore
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active May 18th 2019

felt like archiving a quote by Paul Taylor somewhere, it is now at

*folklore*.Besides being funny, it is actually a useful comment for the newbie, and so I linked to it from

*category theory*.

- Discussion Type
- discussion topicFQFT
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 18th 2019

I am beginning to give the entry

*FQFT*a comprehensive*Exposition and Introduction*section.So far I have filled some genuine content into the first subsection

*Quantum mechanics in Schrödinger picture*.But I have to quit now. This isn’t even proof-read yet. So don’t look at it unless you feel more in editing-mood than in pure-reading-mood.

- Discussion Type
- discussion topicaugmented simplicial set
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by atmacen
- Last Active May 18th 2019

I noticed that augmented simplicial set did not point anywhere, so i created the entry. But have no energy to put anything of substance there right now.

- Discussion Type
- discussion topicvacua -- contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 17th 2019

- Discussion Type
- discussion topicautomorphism of a vertex operator algebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 17th 2019