Simplicial sheaf
WebbFor any pointed simplicial sheaf X in ∆opSh(Sm/k) one defines the A1-homotopy group sheaves, πA1 i(X), to be the sheaves of simplicial homotopy groups of a fibrant replacement of X in the A1-model structure. Morel, in his foundational work in [5, Ch. 6] has defined, for every integer i, A1-homology groups HA1 i(X) and canonical Hurewicz … In mathematics, more specifically in homotopy theory, a simplicial presheaf is a presheaf on a site (e.g., the category of topological spaces) taking values in simplicial sets (i.e., a contravariant functor from the site to the category of simplicial sets). Equivalently, a simplicial presheaf is a simplicial object in the … Visa mer Let F be a simplicial presheaf on a site. The homotopy sheaves $${\displaystyle \pi _{*}F}$$ of F is defined as follows. For any $${\displaystyle f:X\to Y}$$ in the site and a 0-simplex s in F(X), set Visa mer • Konrad Voelkel, Model structures on simplicial presheaves Visa mer The category of simplicial presheaves on a site admits many different model structures. Some of them are … Visa mer • cubical set • N-group (category theory) Visa mer • J.F. Jardine's homepage Visa mer
Simplicial sheaf
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Webb8 dec. 2024 · simplicial homology generalized homology exact sequence, short exact sequence, long exact sequence, split exact sequence injective object, projective object … Webb20 nov. 2024 · Let X be a locally fibrant simplicial sheaf on the big étale site for k, and let Y be a k scheme which is cohomologically proper. Then there is a Künneth-type isomorphism which is induced by an external cup-product pairing. Reductive algebraic groups G over k are cohomologically proper, by a result of Friedlander and Parshall.
WebbNow X is a simplicial sheaf if for every object U 2Cand R 2 (U) the map ˝ R is an isomorphism (this definition is from [Jardine, 2007, p.37]). Note that an equivalent way to define simplicial sheaves would be as simplicial objects in the category of sheaves. The sim-plicial sheaves form a full subcategory SSh(C) of SPre(C) and there is Webbsheaves are presheaves F satisfying a limit condition F(U) Ÿ= lim €• ž:V !U2R F(V) for all covering sieves R ı hom(U;) of C. A simplicial presheaf (respectively sheaf) is a simplicial object in the category of presheaves (respectively sheaves) on C; a simplicial presheaf is alternatively just a contravariant functor on C taking values in ...
Webb6 apr. 2024 · to be equal in order to do so, and I don't understand how this follows from $\pi_0$, which only knows things at levels 0 and 1 in the simplicial structure. Given, it seems like the key application will have to do with groupoids, for which all data is determined in levels 0 and 1, but I want to know why this works in general. WebbStacks are described as sheaves of groupoids G G satisfying an effective descent condition, or equivalently such that the classifying object BG B G satisfies descent. The set of simplicial sheaf homotopy classes [∗,BG] [ ∗, B G] is identified with equivalence classes of acyclic homotopy colimits fibred over BG B G, generalizing the ...
Webb28 mars 2024 · A local fibration or local weak equivalence of simplicial (pre)sheaves is defined to be one whose lifting property is satisfied after refining to some cover. …
WebbIs there a good way to define a sheaf over a simplicial set - i.e. as a functor from the diagram of the simplicial set to wherever the sheaf takes its values - in a way that while defined on simplex by simplex corresponds in some natural manner to what a sheaf over the geometric realization of the simplicial set would look like? firstclass login ssdecWebb1 maj 2024 · In the introduction to his paper "Flasque Model Structures for Presheaves" (in fact simplicial presheaves) Isaksen states on the top of page 2 that his model structure has a nice characterisation of fibrant objects and that "This is entirely unlike the injective model structures, where there is no explicit description of the fibrant objects". first class limo lunenburgWebb15 sep. 2010 · Matthias Wendt. In this paper, we discuss the construction of classifying spaces of fibre sequences in model categories of simplicial sheaves. One construction proceeds via Brown representability and provides a classification in the pointed model category. The second construction is given by the classifying space of the monoid of … first class llbWebbthe simplicial sheaf K(F, n) is an Eilenberg—MacLane complex. Recall also that the homotopy category Ho(Sch \k)et is constructed by formally inverting morphisms repre … firstclass login nlcWebbwhich is defined for any abelian sheaf A on the ´etale site for k. Here, L varies through the finite Galois extensions of k, and we write G = Gal(L/k) for the Galois group of such an extension L. Here, the scheme Sp(L) is the Zariski spectrum of the field L. The simplicial sheaf EG ×G Sp(L) is the Borel construction for the action of first class local train passWebbA simplicial sheaf (resp. simplicial presheaf) X is a simplicial object in the category of sheaves (resp. presheaves). In other words, Xis a con-travariant functor op!Shv(C), where … first class lie flat seatsWebb22 feb. 2001 · The present paper defines stacks (from several points of view) as sheaves of groupoids satisfying an e#ective descent condition, and then discusses the basic homotopy theoretic properties of... first class limo service