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added the pointers to the combinatorial proofs of the fiberwise detection of acyclicity of Kan fibrations, currently discussed on the AlgTop list, to the nLab here.
added reference to dendroidal version of Dold-Kan correspondence
I have expanded vertex operator algebra (more references, more items in the Properties-section) in partial support to a TP.SE answer that I posted here
I took the liberty of incorporating material from Andre Joyal's latest message to the CatTheory mailing list into the entry dagger-category:
created sections
cross-linked with t-structure (here)
the entry Dold-Kan correspondence and several related entries had long been asking for connective chain complex. I have now started something there. Of course this can be much further expanded on…
a small entry to make room for the notion of -connectivity with respect to t-structures, to cross-link entries such as connective chain complex and connective spectra, and to disambiguate from “-connected object”.
I am removing all redirects for “connective” from this entry, in order to make room for a dedicated entry “n-connective object” which makes room for disambiguation with the notion of connectivity in stable -categories with t-structure.
added pointer to today’s:
wrote something at Nullstellensatz, prompted by this old MO comment by Lawvere.
Spurred by an MO discussion, I added the observation that coproduct inclusions are monic in a distributive category.
stub for cosmic inflation (for the moment just to record some references)
I am giving Hovey’s book a category:reference-entry, as demanded by Dmitri in pointed model category
Added
added pointer to:
I have polished category of chain complexes a little more and started a section (but unfinished) with discussion of that and how is itself again an abelian category
added pointer to
added these pointers on classification of topological phases of matter via tensor network states:
C. Wille, O. Buerschaper, Jens Eisert, Fermionic topological quantum states as tensor networks, Phys. Rev. B 95, 245127 (2017) (arXiv:1609.02574)
Andreas Bauer, Jens Eisert, Carolin Wille, Towards a mathematical formalism for classifying phases of matter (arXiv:1903.05413)
Linked to from https://ncatlab.org/nlab/show/orthogonal+factorization+system and https://ncatlab.org/nlab/show/final+functor
Todo: add more proofs of this result.
For some reason the xymatrixes were causing errors so I had to comment them out to submit. Here is an example error:
An error occurred when running pdflatex on the following diagram. \xymatrix@=5em{e \ar[r]^\gamma \ar[dr]_{\gamma’} & GFc \ar[d]^{Gf} \ & GFc’} The error was: Timed out
How can I fix this?
I strongly disagree with the statement in Grothendieck category that the Grothendieck category is small. The main examples like are not! What did the writer of that line have in mind ?
added pointer, here and in related entries, to
being one of the early references considering the computation of black hole radiation in terms of thermal field theory on Wick-rotated spacetimes with compact/periodic “Euclidean time”.
at KLT relations I have expanded the list of references. I added also references for the generalization of these relations that is known these days as “gravity is Yang-Mills squared” or similar (eventually this might want to be a separate entry).
In this course I also expanded the list of references at quantum gravity – As a perturbative quantum field theory
found this article as well, going to merge lattice (in a vector space, etc.) into here
Anonymous
added pointer to:
and publication data for:
Thomas Holder has been working on Aufhebung. I have edited the formatting a little (added hyperlinks and more Definition-environments, added another subsection header and some more cross-references, cross-linked with duality of opposites).
Stub, redirects Newman’s theorem.
added pointer to the landing page (www.wolfram.com/mathematica) and cross-link with Stephen Wolfram
added to n-excisive functor a section
starting a dedicated entry for the category of vector bundles with homomorphisms allowed to cover non-trivial base maps (while previously we only had VectBund(B) for fixed base ).
For the moment the main point is to record the interesting cartesian- and tensor-monoidal structure (now here)
I found it was time to have a general table of contents bundles - contents to be added as a floating table to the relevant entries. So I started one.
Created semi-simplicial set, mainly as a repository for some terminological remarks. I would welcome anyone more knowledgeable about the history to correct or improve it!
a fairly trivial entry, for the purpose of easing the hyperlinking in entries like bireflective subcategory, parameterized spectra, VectBund, etc.
Added the reference now that it has appeared: