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am adding references, such as this one:
added a paragraph and a reference to cup product, archiving the blog comment here
added references by Pronk-Scull and by Schwede, and wrote an Idea-section that tries to highlight the expected relation to global equivariant homotopy theory. Right now it reads like so:
On general grounds, since orbifolds are special cases of stacks, there is an evident definition of cohomology of orbifolds, given by forming (stable) homotopy groups of derived hom-spaces
into any desired coefficient ∞-stack (or sheaf of spectra) .
More specifically, often one is interested in viewing orbifold cohomology as a variant of Bredon equivariant cohomology, based on the idea that the cohomology of a global homotopy quotient orbifold
for a given -action on some manifold , should coincide with the -equivariant cohomology of . However, such an identification (1) is not unique: For any closed subgroup, we have
This means that if one is to regard orbifold cohomology as a variant of equivariant cohomology, then one needs to work “globally” in terms of global equivariant homotopy theory, where one considers equivariance with respect to “all compact Lie groups at once”, in a suitable sense.
Concretely, in global equivariant homotopy theory the plain orbit category of -equivariant Bredon cohomology is replaced by the global orbit category whose objects are the delooping stacks , and then any orbifold becomes an (∞,1)-presheaf over by the evident “external Yoneda embedding”
More generally, this makes sense for any orbispace. In fact, as a construction of an (∞,1)-presheaf on it makes sense for any ∞-stack, but supposedly precisely if is an orbispace among all ∞-stacks does the cohomology of in the sense of global equivariant homotopy theory coincide the cohomology of in the intended sense of ∞-stacks, in particular reproducing the intended sense of orbifold cohomology.
At least for topological orbifolds this is indicated in (Schwede 17, Introduction, Schwede 18, p. ix-x, see also Pronk-Scull 07)
added graphics of the light hadron masses from Fodor-Hoelbling 12
have split off tensor product of abelian groups from tensor product and expanded slightly
As far as I can tell, Ehrhard’s definition of comprehension requires not just that the fibers have terminal objects but that these are preserved by the reindexing functors. This is automatic if the fibration is a bifibration, as in Lawvere’s version; it’s fairly explicit in Ehrhard’s formulation, and somewhat implicit in Jacobs’ but I believe still present (his “terminal object functor” must, I think, be a fibered terminal object).
I added some references to continuation-passing style, as well as a big rambling Idea section.
added to identity type a mentioning of the alternative definition in terms of inductive types (paths).
Added a subsection to cartesian closed category, the functional completeness theorem. (To be expanded upon, eventually.)
brief category:people-entry for hyperlinking references at Higgs field, flavour anomaly, and asymptotic safety (or not).
added a brief historical comment to Higgs field and added the historical references
Edit to: standard model of particle physics by Urs Schreiber at 2018-04-01 01:15:37 UTC.
Author comments:
added textbook reference
Just noticed that when this page is shown in a Google search, the link from the Google page does not work. It seems that the “+” sign that used to be in the entry title gets interpreted as a whitespace.
Therefore I am now changing the page name, replacing “+” by “and”. This should fix the problem, once Google picks up the change.
This page is dedicated to the Stieltjes integral. It is basically a generalization of integrals with respect to a function of bounded variation.
This page will present the main propperties of the Stieltjes integral and show its links with measure theory and other types of integral, mainly the Riemann integral, the Lebesguye integral and the Stieltjes integral.
I merged coherent formula into coherent logic and added redirects; I didn’t see a good reason to keep them separate. Perhaps the page should actually be called coherent theory to match with geometric theory, or vice versa, any thoughts?
I thought it better to use rather than in the addition, since it’s supposed to apply to .