Simplicial sheaf
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 … Webb8 dec. 2024 · simplicial homology generalized homology exact sequence, short exact sequence, long exact sequence, split exact sequence injective object, projective object …
Simplicial sheaf
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WebbA simplicial -module (sometimes called a simplicial sheaf of -modules) is a sheaf of modules over the sheaf of rings on associated to . We obtain a category of simplicial … WebbSuitably formulated, we can associate to a simplicial sheaf Xa simplicial sheaf of monoids consisting of homotopy self-equivalences of X. To this monoid we can apply the bar construction. One can prove that the resulting space classifies fibre sequences of simplicial sheaves. In our approach to the construction of classifying spaces, we introduce
Webb8 jan. 2016 · Jan 8, 2016 at 19:46 Like a sheaf takes values in Set, a simplicial sheaf takes values in simplicial sets. What your lecturer was talking about was a sheaf (set-valued) defined on a simplicial set, which amounts to regarding the simplicial set as a topological space (via it's geometric realization). 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?
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 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.
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 ...
Webb15 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 … northfield ct mapWebbA 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 … northfield ct hoodieWebbsimplicial sheaves of groups because we can check it at each point. Last, note that the de nition BG n = Gn only depended on the multiplication in G. In particular, we could do the … northfield ct property cardsWebbFor 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 … northfield ct zip codeWebbBetter: A simplicial ring A • is a sheaf on Δ (the category of finite ordered sets endowed with the chaotic topology). Then a simplicial module over A • is just a sheaf of modules. … how to save webp file as pngWebb23 maj 2024 · model structure on simplicial presheaves descent for simplicial presheaves descent for presheaves with values in strict ∞-groupoids Constructions structures in a … how to save web shortcut to desktopWebb22 feb. 2001 · On the other hand, given a cocycle * Theorem 7 is a generalization of Theorem 16 of [10], which deals with the case where G is a sheaf of groups and X is a … how to save webpage to desktop