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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 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 connection constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality education elliptic-cohomology enriched fibration 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 infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal-logic model model-category-theory monads monoid monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories 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 stack 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 topicSimple homotopy theory
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Dec 6th 2011

Partially spurred on by an MO question, I have started an entry on simple homotopy theory. I am also intrigued as to whether there is a constructive simple homotopy theory that may apply in homotopy type theory, but know so little (as yet) about that subject that this may be far fetched.

- Discussion Type
- discussion topicexact functor
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Mike Shulman
- Last Active Dec 6th 2011

added to exact functor the characterization of left exact functors as those preserving terminal object and pullbacks. This was previously stated only at finitely complete category.

- Discussion Type
- discussion topicAT category + Steve Lack
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by Todd_Trimble
- Last Active Dec 5th 2011

Steve (Lack) has put a comment box on AT category. I have not been following that entry so am not able to reply to his point.

- Discussion Type
- discussion topic1d WZW model
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 5th 2011

placeholder for 1d WZW model, to be expanded

- Discussion Type
- discussion topicn-truncated object in an (oo,1)-category
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Dec 5th 2011

I filled in content at n-truncated object of an (infinity,1)-category.

to go with my discussion with David Roberts. I had planned to go further and also write the entry on Postnikov twoers, but got distracted all day.

Apart from that I just added this link to Higher Topos Theory and did some editing there, added a table of contents, expanded the floating toc.

- Discussion Type
- discussion topicDream mathematics
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by TobyBartels
- Last Active Dec 4th 2011

Heard the rumours and wondered what it is? Now you know.

- Discussion Type
- discussion topicReflexive Banach space
- Category Latest Changes
- Started by Yemon Choi
- Comments 9
- Last comment by TobyBartels
- Last Active Dec 4th 2011

I started editing the page on reflexive Banach spaces - in particular I corrected the definition and stuck in a mention of "James space". A link or reference is needed but I am currently a bit too frazzled/stressed to do further editing today.

- Discussion Type
- discussion topicDHR category
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Tim_Porter
- Last Active Dec 2nd 2011

I have expanded at DHR category the Idea-section and added more hyperlinks.

- Discussion Type
- discussion topiclocalized endomorphism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 1st 2011

I have given the definition of localized endomorphism its own entry (it is otherwise sitting inside DHR superselection theory).

- Discussion Type
- discussion topicJacobian
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Nov 30th 2011

stub for Jacobian

- Discussion Type
- discussion topicOutside, looking in
- Category Latest Changes
- Started by Tom Leinster
- Comments 59
- Last comment by Todd_Trimble
- Last Active Nov 30th 2011

Joel Hamkins and Andy Putman made some comments about the nLab on MathOverflow, beneath an answer by Andrew.

It’s interesting to know what people’s perceptions are, even if they’re wrong. (And I would think that Andy P’s perception

*is*wrong.) I don’t know what Andrew S has in mind when he says that Joel’s point is extremely easy to answer.

- Discussion Type
- discussion topicContractibility of embedding spaces
- Category Latest Changes
- Started by Andrew Stacey
- Comments 6
- Last comment by Andrew Stacey
- Last Active Nov 30th 2011

Following a discussion on the algebraic topology list, I’ve written a proof of the contractibility of the space of embeddings of a smooth manifold in a reasonably arbitrary locally convex topological vector space. The details are on embedding of smooth manifolds and it also led to me creating shift space (I checked on MO to see if there was an existing name for this, and Bill Johnson said he hadn’t heard of it).

- Discussion Type
- discussion topic(infinity,n)Cat
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 30th 2011

added the recent Barwick/Schommer-Pries preprint to (infinity,n)Cat, together with a few more brief remarks.

- Discussion Type
- discussion topictwisted bundle
- Category Latest Changes
- Started by Urs
- Comments 28
- Last comment by Urs
- Last Active Nov 28th 2011

I have been working on the entry twisted bundle.

Apart from more literature, etc. I have started typing something like a first-principles discussion: first a general abstract definition from twisted cohomology in any cohesive $\infty$-topos, then unwinding this in special cases to obtain the traditional cocycle formulas found in the literature.

Needs more polishing here and there, but I have to pause now.

- Discussion Type
- discussion topicMaurer-Cartan equation
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Nov 28th 2011

I have added to Maurer-Cartan equation a brief section MC elements in L-infinity algebras and then a Properties section As homomorphisms of L-infinity algebras where I explain how MC elements are secretly homs of dg/$L_\infty$-algebras.

- Discussion Type
- discussion topicLie bialgebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Nov 28th 2011

created Lie bialgebra, but so far just a comment on their quantization.

- Discussion Type
- discussion topicC-infinity algebra
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Nov 28th 2011

I noticed that we are lacking C-infinity algebra, so I very briefly created a very stubby stub (no time right now…)

- Discussion Type
- discussion topiccooperad
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 28th 2011

stub for cooperad

- Discussion Type
- discussion topicconnected object
- Category Latest Changes
- Started by Todd_Trimble
- Comments 2
- Last comment by Urs
- Last Active Nov 28th 2011

Added a new Properties section to connected object. Including a theorem which is a bit of a hack (where I leave it to others to decide if ’hack’ should be interpreted positively or negatively!).

- Discussion Type
- discussion topicparallel transport
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by jim_stasheff
- Last Active Nov 26th 2011

wrote parallel transport (which was previously redirecting to connection on a bundle).

Also rewrote Dyson formula.

- Discussion Type
- discussion topicsyntax and semantics
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 25th 2011

while polishing up type theory - contents I felt the need for entries called syntax and semantics. I have created these just so that the links to them are not grey, but I put in only something minimalistic . I could add some general blah-blah, but I’d rather hope some actual expert feels inspired to start with some decent paragraphs.

- Discussion Type
- discussion topicproofs as programs
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 24th 2011

created proofs as programs

- Discussion Type
- discussion topicbicategorical pasting
- Category Latest Changes
- Started by Todd_Trimble
- Comments 2
- Last comment by Todd_Trimble
- Last Active Nov 23rd 2011

Added to pasting diagram a reference to the bicategorical pasting theorem given by Verity in his thesis.

- Discussion Type
- discussion topic(hyperconnected,localic) factorization system
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 22nd 2011

just for completness, I have split off a brief entry (hyperconnected,localic) factorization system.

- Discussion Type
- discussion topicfactorization systems - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 20th 2011

I have created a list factorization systems - contents and included it as a “floating TOC” into the relevant entries.

- Discussion Type
- discussion topicnormal field etension
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Nov 20th 2011

Created a stub for normal field extension. (and missed out the x in the title of this page.)

- Discussion Type
- discussion topicnotions of subcategory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 19th 2011

have created a “floating TOC”

*notions of subcategory*and have included it in the relevant entries

- Discussion Type
- discussion topicindexed adjoint functor theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 18th 2011

stub for indexed adjoint functor theorem

- Discussion Type
- discussion topicreflective factorization system
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 17th 2011

In the Definition-section at reflective factorization system I found the “$\Psi$” and “$\Phi$” used in the text oppositely to how they appear in the displayed diagram. I think I have fixed this.

- Discussion Type
- discussion topicStiefel-Whitney class
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by TobyBartels
- Last Active Nov 16th 2011

added to Stiefel-Whitney class briefly the definition/characterization.