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wrote a few lines at differential calculus, just so that the link does point somewhere. Clearly just a stub, to be expanded.
started self-dual higher gauge theory. Just minimal idea and list of references so far.
crated D'Auria-Fre formulation of supergravity
there is a blog entry to go with this here
I am starting something on U-duality at supergravity.
But all still very skeletal at the moment.
Added a (sketchy) pointer to
have added to conjugation action a detailed exposition of how the conjugation action is the internal hom of actions, here.
Thanks to a Guest comment here I looked at this page for essentially the first time, and realized that it’s one more thing that’s naturally done in linear constructive mathematics (“complemented subsets” or “disjoint pairs” are the elements of the linear powerset).
One question: this page says that the disjoint pairs form a “Boolean rig”, but that doesn’t seem right to me. A Boolean rig would, I presume, lack a negation operation entirely; but here we do have an involutive “negation” even though it’s not the “additive inverse”. I would say that the disjoint pairs form a De Morgan algebra, and in fact more generally a *-autonomous lattice. Am I misinterpreting the intended meaning of “Boolean rig”?
Also, what is the “Handbook of Constructive Analysis” referred to (as a graylink from Bishop \& Bridges)? I can’t find it on google.
I created this article so that links from Cheng space point to an actual article on the nLab.
The entry monomorphism used to start off saying that a monomorphism is an epimorphism in the opposite category…
I have polished and expanded the text now, trying to make it look more like an actual exposition and explanation. I have also expanded a little the Examples-section, and similarly at epimorphism.
These weird kind of entries date from the early days of the nLab, when none of us saw yet what the nLab would once be. Back then it was fun to proceed this way, now it feels awkward.
I hereby pose a challenge to the nForum community:
I challenge you to each pick one entry on a basic topic (nothing fancy), go to the corresponding nLab entry and give it a gentle introductory Idea-section, make sure that the basic motivating examples are mentioned in the order in which the newbie needs to see them, and that the key facts are stated as nicely discernible propositions, best with proof or at least with some helpful pointer, in short, to make the entry a useful read for those readers who would profit from reading it, especially those who do not know the nPOV yet, but might be guided to learn and appreciate it.
added this pointer:
Added a mentioning of the term logos at the beginning of Heyting category.
wrote an entry Deligne’s theorem on tensor categories on the statement that every regular tensor category is equivalent to representations of a supergroup. Added brief paragraphs pointing to this to superalgebra and supersymmetry, added cross-links to Tannaka duality, Doplicher-Roberts reconstruction etc. Also created a disambiguation page Deligne’s theorem
added pointer to today’s
a bare list of references, to be !include-ed into the References-sections of relevant entries (such as at anyons and at topological order)
The list means to bring out the wide-spread consideration, in theoretical articles, of anyons whose positions in real space vary on a torus (or even higher genus surfaces) instead of a plane – an assumption that is necessary for many of the intended theoretical conclusions to be valid, but rather dubious as an assumption about actual physical systems (away from simulation).
The preprint by Gaiotto & Johnson-Freyd at the end is one of the few places that I am aware of where this assumption is questioned, and I included a couple of paragraphs of quote.
(This all in preparation for an article pointing out that anyonic states can in principle be localized also in more abstract spaces than “position space”, some of which are naturally toroidal, such as the case of reciprocal momentum space for which I took the liberty of pointing to our existing 2206.13563.)
Needed to refer within the circle of pages in algebraic geometry
A notion in algebraic geometry.
I just noticed and noted that Gabriella Böhm wrote a book, on generalizations in Hopf world,
Added a reference to today’s
added pointer to:
Add reference to marked 2-limit.
I created hypermonoid, polishing the comments I made in the hypermonoid thread into an article. The last subsection of the article mentions a general technique for constructing hypermonoids which ought to immediately suggest further examples to a quantum group specialist like Zoran, but I am not such a specialist. I also inserted some shameless self-promotion under References.
Removed the sentence
“If X has decidable equality, then the negation of equality is a (in fact the unique) tight apartness on X, and any function from X to any set Y (with any tight apartness on Y) must be strongly extensional.”
because is not true. Assuming WLPO, Cantor space has decidable equality but the negation of equality is still not the tight apartness relation on Cantor space.
Anonymouse
Created doctrinal adjunction. The page could probably use some examples and/or fleshing out.
created directed homotopy type theory
added a Properties-section to pullback
Where does this concept come from? The page lists no relevant references, nor can I find any search results for “quadrable cospan”. Furthermore, the “Note on terminology” mentions the terminology “carrable”, which means something different as far as I can tell (and certainly in the cited references): namely, a morphism along which all pullbacks are admitted.
Fixed/clarified the notation in the definition of local objects in a model category. Added references.
Also added references to (infinity,1)-categorical hom-space in that context.
added pointer to Sorokin 01