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Definition
Presentation over a site
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geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
In generalization of how a smooth ∞-groupoid is an ∞-groupoid equipped with generalized smooth structure modeled on Cartesian spaces with smooth functions between them (hence: on smooth manifolds), a singular-smooth -groupoid carries geometric structure which, in addition to being smooth almost everywhere, may have orbi-singularities, in that it is locally modeled on Cartesian space regarded possibly as -fixed loci for any finite group .
Write
for the category of Cartesian spaces with smooth functions between them, regarded as a site via the coverage of differentiably good open covers,
for the (2,1)-category of groupoids which are deloopings of finite groups, regarded as an -site via the trivial topology.
Then singular-smooth -groupoids are the objects in the hypercomplete -sheaf -topos over the product of these sites:
In generalization of how smooth -groupoids form a cohesive -topos over , so singular-smooth -groupoids form a singular-cohesive -topos.
Where the cohesive -topos is the natural home of smooth manifolds and diffeological spaces, reflecting their differential cohomology, so is the natural home of orbifolds reflecting their proper orbifold cohomology (SaSc 2020).
Last revised on October 26, 2021 at 10:56:13. See the history of this page for a list of all contributions to it.