Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
started a Properties-section at Lawvere theory with some basic propositions.
Would be thankful if some experts looked over this.
Also added the example of the theory of sets. (A longer list of examples would be good!) And added the canonical reference.
Erased the reference of Edgar Brown which is misplaced here in version 9.
P.S. The link to Brown’s webpage does not seem to work.
following Zoran’s suggestion I added to the beginning of the Idea-section at monad a few sentences on the general idea, leading then over to the Idea with respect to algebraic theories that used to be the only idea given there.
Also added a brief stub-subsection on monads in arbitrary 2-categories. This entry deserves a bit more atention.
Created stub for Wu manifold, which is now linked on rational homology sphere.
Stub, for now just to record relevant references. Related to the recently added entry Magnus expansion and also to pre-Lie algebra.
category: people page for the reference
Anonymouse
Jim Stasheff pointed out a reference that discusses categorifications of associahedra. I added the ref to associahedron
After this discussion at string diagrams for linearly distributive categories with unit = counit, I finally got round to having a go at making star-polycategory. Still much more to do. Hopefully I didn’t make any major mistakes so far.
we were lacking an entry realizability that points to all the related entries (and in fact some entries were asking for just “realizability”).
So I started one. Put in the following Idea-paragraph:
The idea of realizability is essentially that of constructivism, intuitionistic mathematics and the propositions as types paradigm: for instance constructively a proof of an existential quantification consists of constructing a specific and a proof of , which “realizes” the truth of the statement, whence the name (e.g. Vermeeren 09, section 1).
Clean up a couple parenthetical remarks. The page ring object seems to indeed have the desired diagrams.
a stub, just to finally make the link work (which has been requested for ages at inhabited set, dominance and inhabited object)
I have made some trivial edits to the wording, hoping to make it flow more nicely.
By the way, this entry is linking (at least now that I adjusted the plural redirect) to recursive function. This is only natural, but – unfortunately – our entry recursive function is empty (and always has been)!
Much of the material needed there is at partial recursive function. We should either put redirects or (better) add a little bit of content to recursive function.
I have added (here) pointer to:
(This edit prompted by discussion in another thread of the same name: here)
I was going to start game semantics to record a couple of references to dependent type theory, but I’m getting an error message at the moment. So I’ll just leave here for now:
In logic, game semantics is used to provide a semantic interpretation of logic constructions in terms of strategies for opposing players to win a game corresponding to some proposition.
For attempts to formulate a game semantics for dependent type theory, see
Matthijs Vakar, Radha Jagadeesan, Samson Abramsky, Game Semantics for Dependent Types, (pdf)
Norihiro Yamada, _Game Semantics for Martin-Löf Type Theory, (arXiv:1610.01669)
Created complete small category, and moved the proof of Freyd’s theorem to there from adjoint functor theorem.
Edited the text in the Idea-section, such as to make the terms monoidal category, monoid objects, module objects appear.
I have added the following paragraph to calculus of constructions, I’d be grateful if experts could briefly give me a sanity check that this is an accurate characterization:
More in detail, the Calculus of (co)Inductive Constructions is
a system of natural deduction with dependent types;
with the natural-deduction rules for dependent product types specified;
and with a rule for how to introduce new such natural-deduction rules for arbitrary (co)inductive types.
and with a type of types (hierarchy).
I fixed a strange link at John Power.
Expanded the entry by more references.
I have erased two redirects which used to be (probably) in Greek but some Lab upgrade has obliterated the difference between the characters and now it was ????? or alike and the info is lost. If somebody has his Greek spelling can ressurect the redirects. I have now changed the page name to his arXiv spelling and put Ioannis Vlassopoulos as a redirect.
a stub entry, for the moment just so as to give a home to these two references:
Hiroshi Kihara, Model category of diffeological spaces, Journal of Homotopy and Related Structures, (2018), 1-40 (arXiv:1605.06794)
Tadayuki Haraguchi, Kazuhisa Shimakawa, A model structure on the category of diffeological spaces (arXiv:1311.5668)
added pointer to:
added this second-order-quote:
Chen Ning Yang writes in C. N. Yang, Selected papers, 1945-1980, with commentary, W. H. Freeman and Company, San Francisco, 1983, on p. 567:
In 1975, impressed with the fact that gauge fields are connections on fiber bundles, I drove to the house of S. S. Chern in El Cerrito, near Berkeley… I said I found it amazing that gauge theory are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added: “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”
added pointer to this article on the arXiv today:
A hint for a relation to tmf, vaguely in line with the lift of the Witten genus to the string orientation of tmf:
added pointer to today’s
added this pointer:
gave 2d TQFT a slightly more informative Idea-section, highlighting the difference between the classical strict case classified by Frobenius algebras and the local/extended non-compact case classified by Calabi-Yau objects.
Added a reference by Abrams as a candidate for a first rigourous proof of the classification result via Frobenius algebras, and added citations for the local case (copied over from TCFT).
added pointer to today’s
added these pointers
Discussion of quantum anomaly cancellation and 7d Horava-Witten theory is in
{#GherghettaKehagias02} Tony Gherghetta, Alex Kehagias, Anomaly Cancellation in Seven-Dimensional Supergravity with a Boundary, Phys.Rev. D68 (2003), 065019, (arXiv:hep-th/0212060)
Spyros D. Avramis, Alex Kehagias, _Gauged Supergravity on the Orbifold (arXiv:hep-th/0407221)
T.G. Pugh, Ergin Sezgin, Kellogg Stelle, / Heterotic Supergravity with Gauged R-Symmetry (arXiv:1008.0726)
Added pointer to today’s
Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt, Maximal supergravities from higher dimensions [arXiv:2309.07232]
Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt, Consistent truncation of eleven-dimensional supergravity on [arXiv:2309.07233]