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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 topicfermionic path integral
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 10th 2011

notes for fermionic path integral

in the course of this also created Pfaffian, added a line to Berezinian integral and linked to everything from various places.

- Discussion Type
- discussion topicThree Roles of Quantum Field Theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active May 10th 2011

created reference-entry Three Roles of Quantum Field Theory

- Discussion Type
- discussion topicMorita morphism
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by DavidRoberts
- Last Active May 9th 2011

since I needed the link to exist, I have created a stub for Morita morphism (of Lie groupoid)s. Made Hilsum-Skandalis morphism redirect to it, for the moment.

- Discussion Type
- discussion topicChern-Weil theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active May 9th 2011

tried to polish a bit the matrial at Chern-Weil theory.

(not that there is much, yet, but still)

- Discussion Type
- discussion topicuniversal connection
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 8th 2011

stub for universal connection (just to record the references for the moment)

- Discussion Type
- discussion topicD-affinity
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 8th 2011

Affinity in the context of D-modules, as defined by Alexander Beilinson is the subject of a new stub D-affinity. There is a categorical generalization in the MPI1996-53 preprint (pdf) of Lunts and Rosenberg in terms of differential monads. Many generalizations of Beilinson-Bernstein localization theorem have their intuitive explanation in a two-step reasoning. First the noncommutative algebra in question is understood as a noncommutative (or maybe categorical) resolution of singularities of a commutative object. Then the latter satisfies D-affinity and one can localize.

- Discussion Type
- discussion topicdomain globalization
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active May 8th 2011

New entry domain globalization of functors (zoranskoda) under development. The codomain globalization is more trivial. This are questions of extending the constructions related to Beck’s comonadicity from categories to functors. Our interest with Gabi Bohm are mainly for covers by localizations with some equivariance/compatibility with respect to additional (co)monad, which are a matter of ongoing work. This compatibility is like, or some dual of the one in the definition of morphisms of Q-categories and also the compatibility of differential monads and localization, studied by Lunts and Rosenberg. The latter is related to the classical fact that the assignment of ring of regular differential operators to a commutative ring $R\mapsto Diff(R)$ is compatible with exact localizations, in the sense that $S^{-1}R \mapsto S^{-1}Diff(R)$; and also to Beilinson’s notion of D-affinity.

- Discussion Type
- discussion topicNoether's theorem
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Eric
- Last Active May 8th 2011

created Noether’s theorem – no-nonsense version

- Discussion Type
- discussion topic(n,r)-logic
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 7th 2011

I have created stubs for the missing entries to complete this table:

The main actual content I added are, (at 2-type theory and 2-logic): pointers to Dan Licata’s thesis and to Mike’s personal wiki pages.

I’d hope that one outcome of the present $n$Café discussion is that eventually some of these entries get equipped with some useful content.

(P.S. I would have linked to material by Mike Stay, too, but I don’t know what to link to.)

- Discussion Type
- discussion topiclocally algebra-ed topos
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Mike Shulman
- Last Active May 7th 2011

I am about to create an entry called locally algebra-ed topos in the spirit of the section for local algebras at classifying topos.

I tend to think this terminology is better than the undescriptive “structured topos”, but please let me know what you think.

I would like to amplify the following fact:

if we agree to say (which is reasonable) that

an

*algebra*is a model of some essentially algebraic theory, hence a lex functor out of a finite-limite category;a

*local algebra*with respect to a coverage on the category is such a lex functor that preserves covers.

then the statement is:

- geometric theories are equivalently theories of local algebras.

- Discussion Type
- discussion topicvariational caclulus - contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 6th 2011

I have started a new subject complex variational calculus - contents and have included it as a floating TOC into relevant entries

- Discussion Type
- discussion topiccharge
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 6th 2011

stub for charge

- Discussion Type
- discussion topicdifferential monad
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active May 6th 2011

I started an important entry differential monad. According to Lunts-Rosenberg MPI 1996-53 pdf differential calculus on schemes and noncommutative schemes can be derived from the yoga of coreflective topologizing subcategories in the abelian category of quasicoherent sheaves on the scheme, like the $\mathbb{T}$-filtration, and $\mathbb{T}$-part, in the case when the topologizing subcategory is the diagonal in the sense of the smallest subcategory of the category of additive endofunctors having right adjoint which contains the identity functor – in that case we say differential filtration and differential part. The regular differential operators are the elements of the differential part of the bimodule of endomorphisms. Similarly, one can define the conormal bundle etc.

- Discussion Type
- discussion topic[[cartesian category]]
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by SridharRamesh
- Last Active May 6th 2011

I’ve disambiguated links to cartesian category. I suggest that we avoid this term.

- Discussion Type
- discussion topiccoherent (oo,1)-operad
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active May 5th 2011

stub for coherent (infinity,1)-operad

- Discussion Type
- discussion topicnew entries
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active May 4th 2011

Created a stubby entry for Gereon Quick, and added some more into (or fixed typos on) Daniel Isaksen, Cech homotopy,profinite homotopy theory and pro-homotopy theory.

- Discussion Type
- discussion topicJon Pridham
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active May 4th 2011

I created an entry for Jonathan Pridham.

- Discussion Type
- discussion topicO-monoidal (oo,1)-category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 3rd 2011

have added to monoidal (infinity,1)-category the definition of $\mathcal{O}$-monoidal $(\infty,1)$-category, for $\mathcal{O}$ an $\infty$-operad

(though maybe this definition either deserves its own entry or ought to be included instead at symmetric monoidal (infnity,1)-category)

- Discussion Type
- discussion topiccategory of factorizations
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by Tim_Porter
- Last Active May 1st 2011

A point of information. These constructions are due to Charles Wells in this particular setting and to Jonathan Leech, (H-coextensions of monoids, vol. 1, Mem. Amer. Math. Soc, no. 157, American Mathematical Society, 1975) in the single object case, and McLane introduces the category of factorisations I think. Charlie Wells even pushes things a bit further than Baues. Hans does not seem to have known of that work. (Charles Wells, Extension theories for categories (preliminary report), (available from http://www.cwru.edu/artsci/math/wells/pub/pdf/catext.pdf), 1979. ) I have been meaning to have a go at this entry as I have written up a modern version of Wells especially in the non-Abelian case. There is a very nice interpretation of Natural System as a lax functor. (I will do this some time…. but I can make the notes available to anyone interested.)

- Discussion Type
- discussion topiccharacteristic class of a structure
- Category Latest Changes
- Started by zskoda
- Comments 5
- Last comment by Urs
- Last Active May 1st 2011

New entry characteristic class of a structure to complement characteristic class and historical note on characteristic classes. I did not link to it from outside so far.

- Discussion Type
- discussion topicuniversally closed morphism
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by Urs
- Last Active Apr 30th 2011

universally closed morphism and improvements at proper morphism

- Discussion Type
- discussion topicproadjoint
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Tim_Porter
- Last Active Apr 30th 2011

New entry proadjoint.

- Discussion Type
- discussion topicnuclear space
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Apr 30th 2011

New stub nuclear topological vector space with redirect nuclear space. Grothendieck’s reference also at Fredholm operator.

- Discussion Type
- discussion topicprime spectrum
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Apr 30th 2011

New entry prime spectrum with redirect Zariski spectrum.

- Discussion Type
- discussion topicFréchet
- Category Latest Changes
- Started by TobyBartels
- Comments 6
- Last comment by Andrew Stacey
- Last Active Apr 28th 2011

Urs created Frechet manifold, so I created Frechet space. (We violated the naming conventions too, but I guess it's OK since we have the redirects in.)

- Discussion Type
- discussion topictoposes as theories
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by zskoda
- Last Active Apr 28th 2011

I am trying to begin to coherently add some of the topics of part D of the Elephant into the Lab.

Currently I am creating lots of stub entries, splitting them off from existing entries if necessary, cross-link them appropriately, and then eventually add content to them.

so far I have for instance created new (mostly stub) entries for things like

I have created

and made it a disambiguation page.

I have edited the linked table of contents at Elephant, etc.

(or rather I will have in a few minutes. All my save-windows are currently stalled. Will have to restart the server.)

- Discussion Type
- discussion topicrepresentable fibered category
- Category Latest Changes
- Started by zskoda
- Comments 6
- Last comment by Urs
- Last Active Apr 27th 2011

New entry representable fibered category.

- Discussion Type
- discussion topicstandard site
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 27th 2011

created standard site (maybe not a great term, but since I am $n$Labifying the Elephant). Added the theorem that every sheaf topos has a standard site of definition to site

- Discussion Type
- discussion topicZariski site
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 27th 2011

have created Zariski site

- Discussion Type
- discussion topicslice category
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Apr 27th 2011

added to overcategory the statement about lifs to adjunctions to slices, here