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This is maybe mainly for entertainment. But don’t forget that for newcomers there is a real issue here which may well be worth explaining:
In mathematics it happens at times that one and the same concept is given two different names to indicate a specific perspective, a certain attitude as to what to do whith such objects.
Here are examples:
A quiver is just a directed graph (pseudograph, to be explicit). But one says quiver instead of directed graph when one is interested in studying quiver representations: functors from the free category on that graph to the category of finite-dimensional vector spaces.
A presheaf is just a contravariant functor. But one says presheaf instead of contravariant functor when one is interested in studying its sheafification, or even if one is just intersted in regarding the category of functors with its structure of a topos: the presheaf topos.
(…)
just a minimum for the moment, in order to record the definition in:
mentioned the -refinement at de Rham theorem
I needed a redirect-kind of entry ordinary homology. So I created one.
I added a couple of references for the claim
There is a Curry–Howard correspondence between linear-time temporal logic (LTL) and functional reactive programming (FRP).
How about for CLT and CLT* (in the computation tree logic section)?
Were we looking to integrate this section with the one above on temporal type theory as an adjoint logic, could there be a way via some branching representation of our type as a tree?
I see Joachim Kock has an interesting way of presenting trees.
created strong adjoint functor
added pointer to:
added rough description and original citation to Adams e-invariant
We should have an entry on large N limit gradually. But sometimes it can be treated as a semiclassical limit. I quoted a reference by Yaffe where I originally read of that approach to the entry semiclassical expansion.
Made a start on an article fixed point, which might need to be farmed out to “sub-pages” (as this is a mighty big general topic).
Cleaning or creating entries related to corings (e.g. grouplike element, Sweedler coring) and entwining structures, including personal entries Gabriella Böhm, Tomasz Brzeziński etc. On the edge of this activity I am interested in the relation between classical correspondence between flat connections and the descent data in abelian context; it could be related to the theorem of Urs and Konrad on the relation between descent data and transport functors in global context. I would like to know the parallel precisely.
Added a cross-reference to algebra for an endomorphism.
added this statement:
Let be a closed smooth manifold of dimension 8 with Spin structure. If the frame bundle moreover admits G-structure for
then the Euler class , the second Pontryagin class and the cup product-square of the first Pontryagin class of the frame bundle/tangent bundle are related by
New entry homological category.
brief note on continuous field of C*-algebras
I gave chromatic homotopy theory an Idea-section.
To be expanded eventually…
Stub entry, for the moment just to have a ace for recording this result:
Nico Brown, Carson Cheng, Tanner Jacobi, Maia Karpovich, Matthias Merzenich, David Raucci, Mitchell Riley, Conway’s Game of Life is Omniperiodic [arXiv:2312.02799]
The Physics arXiv Blog, Mathematicians Prove the “Omniperiodicity” of Conway’s Game of Life (Dec 2024)
creating a bare minimum, for the moment only to give a home to these references:
Nik Weaver, Quantum relations [arXiv:1005.0354]
Nik Weaver, Greg Kuperberg, A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations, Memoirs of the AMS 215 (2011) [ams:memo-215-1010]
for when the editing functionality is back, this here is a good textbook to record at quantization:
a stub entry, to make the link work which had long been requested at George Bergman
Under definition 1 of salamander lemma, I fixed a mistake in the definition of where there was a direct sum of two submodules, where there needed to be a sum (i.e., join) instead.
am starting to work on derived smooth manifold, so far just a little bit on the motivation (correction of limits of manifolds)
I am a bit hesitant to add a lot of details from David Spivak’s article, since it seems evident that there is some room to streamline the constructions. I need to think about how to deal with this. One really wants to just specify the site as a geometry (for structured (infinity,1)-toposes) and then just say that a derived manifold is a derived scheme in the sense descrived at generalized scheme on this.
In section 10.1 David Spivak discusses one reason that prevented him from setting things up this way: actually I think this points to the following general issue with the definition of geometry (for structured (infinity,1)-toposes): instead of a Grothendieck topology generated by admissible morphisms the definition ought to just refer to a coverage by admissible morphisms, and instead of the stability under pullback one ought to just consider the coverage-style stability condition.
More later.