Grothendieck enriched categories
http://sheaves.github.io/slides/Final.pdf WebJun 19, 2016 · The enriched Grothendieck construction gives me a functor C → I, where C is a simplicially enriched category. We can extend this functor along the homotopy coherent nerve h N: s C a t → s S e t, and by Proposition 3.2.5.18 of Higher Topos Theory, we know that there is a corresponding morphism X → N ( I) where X is a simplicial set.
Grothendieck enriched categories
Did you know?
WebApr 19, 2024 · Section 4 quickly recalls the notion of indexed category, together with some basic element of the theory of fibrations and their relation to indexed categories via the Grothendieck construction, with a focus on the case of indexed monoidal categories and monoidal fibrations. WebThe Grothendieck Construction A group G can be treated as a category C =G. A group action G N !N can be treated as a group hom G !Aut(N), or a functor C !Grp; 7!N: Generalizing, we may start with a category C (with many objects) acting on a collection of categories fN cg c2C. i.e. a functor N : C !Cat c 7!N c; (c !gd) 7!(N c !g N d):
WebWe introduce an enriched analogue of Lam and Pylyavskyy’s theory of set-valued -partitions. An an application, we construct a -theoretic version of Stembridge’s Hopf algebra of peak quasisymmetric functions. We show th… Webwe generalize the notion of Grothendieck fibrations of small categories to our enriched categories, whose restriction to metric spaces is a notion called metric fibration that is initially introduced in [15]. It is remarkable that the magnitude of such a fibration is a product of those of the fiber and the base.
WebGiven a group, we construct a fundamental additive functor on its orbit category. We prove that any isomorphism conjecture valid for this fundamental additive functor holds for all additive functors, like -theory, cycl… WebDec 28, 2024 · The natural tensor product operation on finite abelian categories is known as the Deligne tensor product or Deligne box product, introduced in ( Deligne 90 ). For A and B two abelian categories, their Deligne tensor product A \boxtimes B is the abelian category such that for any other abelian category C right exact functors of the form A ...
WebMay 11, 2024 · Grothendieck enriched categories Authors: Yuki Imamura Abstract In this paper, we introduce the notion of Grothendieck enriched categories for categories enriched over a sufficiently nice...
WebMay 13, 2024 · An enriched functor F between two categories C and D, besides mapping objects to objects, also assigns, to every pair of objects in C, a morphism in V: F a b :: C (a, b) -> D (F a, F b) A functor is a structure-preserving mapping. For regular functors it meant preserving composition and identity. canton ga movie theatersWeb5 rows · May 11, 2024 · Then we establish the Gabriel-Popescu type theorem for Grothendieck enriched categories. We also ... canton ga movie theater riverstonehttp://sheaves.github.io/slides/Final.pdf bride price bookhttp://sheaves.github.io/slides/fibrations-comodules.pdf bride price things fall apartWebMay 2, 2024 · Then we establish the Gabriel-Popescu type theorem for Grothendieck enriched categories. We also prove that the property of being Grothendieck enriched categories is preserved under the change... bride price is often found in:WebApr 1, 2024 · The Grothendieck construction is one of the central aspects of category theory, together with the notions of universal constructions such as limit, adjunctionand Kan extension. It is expected to have suitable analogs in all sufficiently good contexts of … canton ga news murderWebThe definition of Grothendieck enriched categories in Definition A is the gen-eralization to enriched categories of the extrinsic characterization of Grothendieck categories given by the Gabriel-Popescu theorem. Hence it is natural to ask if we can characterize … canton garbage pickup schedule