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tried to polish algebraic definition of higher categories a little
brief category:people-entry for hyperlinking references at Higgs inflation and anomalous magnetic moment
brief category:people-entry for hyperlinking a historical reference at gauge theory
(I made “Jean Iliopoulos” a redirect, I hope I got it right that both names are used by the same person)
stub for flop transition (I mean the flop transition in terms of SCFTs. Maybe I should find a more specific title for that)
Quickly generated free topos. Mostly references.
This page just had a couple of references, so I’ve added the idea and more references.
I came to this subject via Lurie’s MO question. Isn’t it a shame that such a highly regarded mathematician reaching out to the categorical logic community doesn’t receive an answer from them?
changed page name to author’s full name (from “jesse” to “Jesse Han”) to comply with convention and avoid ambiguity.
also added this pointer:
Flypitch project – Formal proof of the independence of CH (github:flypitch, pdf)
(formal proof of independence of the continuum hypothesis)
A message to Mike:
Hi Mike,
I hear that in Swansea you ended by talking about things related to elementary ∞-toposes. I didn’t get a chance to see anyone’s notes yets. Do you have electronic notes to share?
brief category:people-enty for hyperlinking references at dark matter
created geometric quantization by push-forward, collecting a bunch of references. Thanks to Chris Rogers for pointers.
created brief entries Wirthmüller context and Grothendieck context, following Peter May’s terminology for the two special cases where four of the Grothendieck six operations specialize to an adjoint triple.
The main thing I’d like to record is lists of classes of examples that realize either of these contexts. But haven’t gotten around to that yet.
brief category:people-entry for hyperlinking references at
Created inductive family. Requires more work, but it’s a start.
added to bipermutative category a remark on the relation to bimonoidal categories and basic examples. But what is still missing are the interesting examples.
brief category:people-entry for hyperlinking references at superstring scattering amplitudes, KLT relations, pure spinor
brief category:people-entry for hyperlinking references at superstring scattering amplitudes, KLT relations, pure spinor
Added something to fill a link. Please check the definition that I have given; it is the one that is most natural to me, but not the most standard! Feel free to add details of equivalent definitions.
The commutative diagram will not render yet, I am working on that now; should be done shortly. [Edit: done now!]
am clearing this page, since I just noticed that it duplicates the entry Robion Kirby. I suppose the latter should be the entry with “Rob Kirby” a redirect(?)
Created page, with definition.
Berger-Mellies-Weber claim that the nerve theorem for monads with arities constructs Eilenberg-Moore and Kleisli objects in the 2-category of categories with arities, but as far as I can see their proof as written only shows that the Eilenberg-Moore adjunction lives in this 2-category, not that it retains its universal property there. Is there a quick way to see that it does? If this is true, then I think it gives an even more “natural” explanation of the nerve construction, along the lines of Tom’s original blog post.
brief category:people-entry for hyperlinking references at table of marks
added pointer to
for computer-checks of the Riemann hypothesis. (there are probably more recent such?)
I gave sheaf with transfer an Idea-section
(the entry used to me named “Nisnevich sheaves with transfer”. I have renamed it to singular to stay with our convention and removed the “Nisnevich” from the title, as the concept of transfer as such is really not specific to the Nisnevich topology).
The idea section now is the following. (Experts please complain, and I will try to fine tune further):
Given some category (site) S of test spaces, suppose one fixes some category Corrp(S) of correspondences in S equipped with certain cohomological data on their correspondence space. Then a sheaf with transfer on S is a contravariant functor on Corrp(S) such that the restriction along the canonical embedding S→Corrp(S) makes the resulting presheaf a sheaf.
Traditionally this is considered for S the Nisnevich site and Corrp(S) constructed from correspondences equipped with algebraic cycles as discussed at pure motive, (e.g. Voevodsky, 2.1 and def. 3.1.1).
The idea is that, looking at it the other way around, the extension of a sheaf to a sheaf with transfer defines a kind of Umkehr map/fiber integration by which the sheaf is not only pulled back along maps, but also pushed forward, hence “transferred” (this concept of course makes sense rather generally in cohomology, see e.g. Piacenza 84, 1.1).
The derived categories those abelian sheaves with transfers for the Nisnevich site with are A1-homotopy invariant provides a model for motives known as Voevodsky motives or similar (Voevodsky, p. 20).
brief category:people-entry for hyperlinking references at Burnside ring and representation ring
Do other people see these final symbols as identical at Serre intersection formula?
Given a regular scheme X and subschemes Y,Z with defining ideal sheaves ℐ,𝒥…
I added a note to the article on the subobject classifier: “In type theory, the type corresponding to the subobject classifier is typically called Prop.”
brief category:people-entry for hyperlinking references at string phenomenology, heterotic string and MSSM
brief category:people-entry for hyperlinking references at G2-manifold and elsewhere