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collected some references on the interpretation of the !-modality as the Fock space construction at !-modality.
Cross-linked briefly with he stub entries_Fock space_ and second quantization.
added to the people-entry Edward Witten a paragraph Fields medal work with a commented list of articles that according to Atiyah won Witten the Fields medal in 1990.
started cubical type theory using a comment by Jonathan Sterling
At simplex I have accompanied the definition of the cellular simplex with that of the topological simplex.
I am pretty much through with expanding and polishing
Now I am starting to work on
So far I have restructured the section outline at these entries to match that of the entry cohesive infinity-groupoid. All these entries are supposed to go through that list of Structures in a cohesive -topos in parallel.
I have also removed at smooth infinity-groupoid a bunch of material that is meanwhile discussed in more polished form at Euclidean-topological infinity-groupoid.
To account for that I should now add a discussion of a free-forgtful adjunction between and and how to transfer structure along that.
added pointer to
where on the bottom of p. 9 I find
Leibniz rejects nilsquare and nilcube infinitesimals, which are alto-gether incompatible with his approach to differential calculus,
So if not Leibniz, who can be credited with first considering nilpotent infinitesimals?
Brief idea of the E-string, pointer to and snippet from one reference that makes it nicely explicit.
I am compiling this and related entries because we have a clean mathematical formalization of this zoo of structures now in terms of equivariant super homotopy theory (as surveyed here). Once everything is cleaned up and published, I will try to go through all the entries and accompany the vague Idea-sections with some solid mathematics.
I have reorganized somewhat entry Maxim Kontsevich (with some new links and few bits of additional info) and created a related stub Vassiliev invariant, just to record a link to an impressive online bibliography maintained by Dror Bar-Natan and Sergei Duzhin, hosted at Duzhin's webpage at Russian Academy of Sciences.
Idea-section and one further reference at Thomason model structure.
I remember Mike once said on the blog somewhere that there might be some problem with Thomason's original claim that cofibrant objects in this structure are posets. I made a brief remark on this, but I can't find Mike's original comment.
brief category:people-entry for hyperlinking references at Kazama-Suzuki model
brief category:people entry for hyperlinking references at Kazama-Suzuki model
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.
brief category:people entry for hyperlinking references at Pontrjagin product
I have touched H-space, slightly expanded here and there and slightly reorganized it.
brief category:people-entry for hyperlinking references at configuration space of points
brief category:people-entry for hyperlinking references at configuration space of points
brief category:people-entry for hyperlinking references at configuration spaces of points
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
Added
I noticed that the entry classifying space is in bad shape. I have added a table of contents and tried to structure it slightly, but much more needs to be done here.
I have added a paragraph on standard classifying spaces for topological principal bundles via the geometric realization of the simplicial space associated to the given topological group.
In the section “For crossed complexes” there is material that had been provided by Ronnie Brown which needs to be harmonized with the existing Idea-section. It proposes something like a general axiomatics on the notion of “classifying space” more than giving details on the geometric realization of crossed complexes
considerably expanded the entry strict 2-group.
Apart from adding an introductory discussion, and expanding the list of examples, in particular by adding that of automorphism 2-groups ...
... I in particular give the detailed translation prescription for how to encode a 2-group by a crossed module at In terms of crossed modules
This is to eventually serve as a supplement to the discussion at nonabelian group cohomology. So I spent some energy on disentangling the four different (though isomorphic) ways a crossed module gives rise to a 2-group (following my article with David Roberts).