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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Added a new Properties section to connected object. Including a theorem which is a bit of a hack (where I leave it to others to decide if ’hack’ should be interpreted positively or negatively!).
splitting this off from su(2)-anyons: Copied much of the material over, but also added a few more sentences.
For the moment this entry is a cautionary tale about confirmation bias more than an entry about physics.
brief category:people-entry for hyperlinking references at tensor hierarchy and at Borcherds algebra
created a quick pointer to, with a brief remark on, spherical T-duality
Finally created funny tensor product. This is not really a very good name for a serious mathematical concept, but I don’t know of a better one.
this is a bare list of references, to be !include-ed into relevant entries (such as D-brane, Dirac charge quantization and D-brane charge quantization in K-theory).
In fact, the list is that which has been in each of these entries all along, and it has been a pain to synchronize the parallel lists. So this here now to ease the process.
just a small mention of unstable K-theory groups of spheres, equivalently homotopy groups of unitary groups
Introducing twisted tensor product
New entry to complement matrix inverse.
wrote something at free abelian group. Not great, need to come back to this.
Skewfield of noncommutative rational functions
Needed at some linear algebra entries including row echelon form.
To use it at Gauss elimination procedure entry.
A generalization of Waldhausen K-theory to dualizable dg-categories and dualizable stable ∞-categories.
For compactly generated inputs, recovers the Waldhausen K-theory of the full subcategory of compact objects.
The formalism is applicable to -presentable stable ∞-categories, where can be uncountable (for example, various categories of sheaves, or categories occurring in functional analysis).
Alexander Efimov, On the K-theory of large triangulated categories, ICM 2022, https://www.youtube.com/watch?v=RUDeLo9JTro
Marc Hoyois, K-theory of dualizable categories (after A. Efimov), https://hoyois.app.uni-regensburg.de/papers/efimov.pdf.
Li He, Efimov K-theory and universal localizing invariant, arXiv:2302.13052.
I was involved in some discussion about where the word “intensional” as in “intensional equality” comes from and how it really differs from “intenTional” and what the point is of having such a trap of terms.
Somebody dug out Martin-Löf’s lecture notes “Intuitionistic type theory” from 1980 to check. Having it in front of me and so before I forget, I have now briefly made a note on some aspects at equality in the section Different kinds of equalits (below the first paragraph which was there before I arrived.)
Anyway, on p. 31 Martin-Löf has
intensional (sameness of meaning)
I have to say that the difference between “sameness of meaning” and “sameness of intenTion”, if that really is the difference one wants to make, is at best subtle.
I finally started linear equation. But am too tired now to really do it justice…
I have added a little bit to supermanifold, mainly the definition as manifolds over superpoints, the statement of the equivalence to the locally-ringed-space definition and references.
added this quote to before the Idea-section:
In the wake of the movement of ideas which followed the general theory of relativity, I was led to introduce the notion of new geometries, more general than Riemannian geometry, and playing with respect to the different Klein geometries the same role as the Riemannian geometries play with respect to Euclidean space. The vast synthesis that I realized in this way depends of course on the ideas of Klein formulated in his celebrated Erlangen programme while at the same time going far beyond it since it includes Riemannian geometry, which had formed a completely isolated branch of geometry, within the compass of a very general scheme in which the notion of group still plays a fundamental role.
[Élie Cartan 1939, as quoted in Sharpe 1997, p. 171]
have expanded the single sentence at differential geometry to something like a paragraph, indicating how differential geometry is the “higher geometry modeled on the pre-geometry ”
Created cartesian multicategory.
starting page on the equivalence type, and moving some information on equivalence in type theory over to this page
Anonymous
Created internal profunctor, which also describes an idea I saw somewhere about internal diagrams in fibrations over the base category. I added what I think are two examples, and asked a generic 'Help!' question. It might be better off on a page of its own, though.
Starting page for one of the authors of the publication
Anonymous