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stub for homotopy type theory
added pointer to:
expanded and polished Kalb-Ramond field. In particular I added more references.
briefly added something to fusion category. See also this blog comment.
expanded model structure on functors by adding a long list of properties
The entry test category which I wrote some time ago, came into the attention of Georges Maltsiniotis who kindly wrote me an email with a kind praise on nlab and noting that his Astérisque treatise on the topic of Grothendieck’s homotopy theory is available online on his web page and that the Cisinski’s volume is sort of a continuation of his Astérisque 301. Georges also suggested that we should emphasise that a big part of the Pursuing Stacks is devoted to the usage of test categories, so I included it into the bibliography and introductory sentence. I hinted to Georges that when unhappy with a state of an nlab entry he could just feel free to edit directly.
this is a bare subsection with a list of references, meant to be !include
-ed into the References-lists of relevant entries (such as AdS-QCD correspondence, AdS-QCD correspondence but also at flux tube and maybe at string)
moving content on dependent extension types from type theory with shapes to its own page here
I have created an entry type of types. Wanted to collect some literature there, but ended up not finding too much…
added pointer to:
added publication details for:
you can define to be the 2-category of all -small categories, where is some Grothendieck universe containing . That way, you have without contradiction.
Do you agree with changing this to
” you can define to be the 2-category of all -small categories, where is some Grothendieck universe containing . That way, for every small category , you have the category an object of without contradiction. This way, e.g. the diagram in Cat used in this definition of comma categories is defined. “
?
Reason: motivation is to have the pullback-definition of a comma category in (For others, it’s about the diagram here) defined, or rather, having Cat provide a way to make it precise. Currently, the diagrammatic definition can either be read formally, as a device to encode the usual definition of comma categories, or a reader can try to consult Cat in order to make it precise. Then they will first find only the usual definition of Cat having small objects only, which does not take care of the large category
used in the pullback-definition. Then perhaps they will read all the way up to Grothendieck universes, but find that option not quite sufficient either since it only mentions Set, but not . It seems to me that large small-presheaf-categories such as can be accomodated, too, though.
(Incidentally, tried to find a “canonical” thread for the article “Cat”, by using the search, but to no avail. Therefore started this one.)
touched the formatting in congruence, fixed a typo on the cartesian square, added a basic example
definition to link to special geometry
am finally splitting this off from Tate curve
Added Eric’s illustrations to the Idea-section at Yoneda embedding.
Added:
Specifically, a continuous functor is a right adjoint functor if and only if it is representable, in which case the left adjoint functor sends the singleton set to the representing object
added pointer to today’s article by Ross Street:
A general abstract formulation of Rost 96 in terms of string diagrams in additive braided monoidal categories is in
I added the remark that the canonical model structure on Cat is the model structure obtained by transferring the projective model structure on bisimplicial sets.
Linking to the page canonical model structure for 2-categories in a couple of places.
Wrote an article Eudoxus real number, a concept due to Schanuel.
a little remark at nonabelian Stokes theorem, still to be expanded
I have expanded the Idea-section at AGT correspondence, saying more explicitly how this may be thought of as regarding the 6d (2,0)-theory as a “2d SCFT with values in 4d SYM theories” and added pointers to further references (including some reviews).
I have similarly expanded/added brief remarks on AGT/generalized S-duality pointing to this at 6d (2,0)-SCFT – Compactification on Riemann surface and at S-duality – for SYM – From compactification