Simplicial sheaf

Author: gkyu

August undefined, 2024

Webb15 aug. 2024 · A sheaf is a certain functor O p e n ( X) o p → C, where C is a 1-category, satisfying a certain limit condition. A stack is a functor O p e n ( X) o p → D, where D is a 2-category, satisfying a more complicated condition. In this case, D is the category of categories and C is the category of sets. – Mark Saving Aug 15, 2024 at 17:51 WebbBetter: 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. …

Cup Products in Sheaf Cohomology Canadian Mathematical …

Webbwhich 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 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 solar wire for sale

model structure on simplicial presheaves in nLab

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 ... Webb22 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... WebbLet X be a ﬁnite simplicial complex. There is a well known linear algebra data description of (constructible with respect to the triangulation) sheaves of vector spaces on X. A … solarwise africa

Stacks and the homotopy theory of simplicial sheaves - Project …

Section 21.41 (09D0): Simplicial modules—The Stacks project

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). solar wireless charger factoriesIn 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 slytherin house quiz

"Webb8 jan. 2016 · 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 sheaf

Simplicial sheaf

Sheaves on a Simplicial Complex - Mathematics Stack Exchange

Webbthe 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 … 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.

Did you know?

Webb22 nov. 2009 · Simplicial sheaves are something else entirely—they're (pre)sheaves of simplicial sets on, say, a category equipped with a Grothendieck topology. I think you … 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 …

Webb1 aug. 2015 · Stacks and the homotopy theory of simplicial sheaves. J. Jardine; Mathematics. 2001; Stacks are described as sheaves of groupoids G satisfying an eective descent condition, or equivalently such that the clas- sifying object BG satisÞes descent. The set of simplicial sheaf homotopy … Expand. 43. PDF. View 1 excerpt; Save. 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 …

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 … WebbThe 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 classical …

Webb19 juni 2024 · The local model structure on simplicial sheaves was proposed in Andre Joyal , Letter to Alexander Grothendieck , 11.4.1984, ( pdf scan ). This is, with BrownAHT …

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 slytherin house prideWebbrooted ﬁbrations of simplicial sheaves. On the other hand, ﬁbrations of simplicial sheaves correspond to principal bundles under homotopy self-equivalences. Suitably 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 … slytherin house quotesWebbSimplicial schemes. A simplicial scheme is a simplicial object in the category of schemes, see Simplicial, Definition 14.3.1. Recall that a simplicial scheme looks like. Here there … solar wireless outdoor speakersWebb28 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. … solar wire management clipsWebb6 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. slytherin house shield coloring pagesWebbContents Introduction 1 Simplicial and Singular Intersection Homology 2 Some Computations 4 Homology with Local Coe cients 6 Some Useful Properties of Intersection Homology 7 Sheaf-Theoretic Intersection Homology 8 INTERSECTION HOMOLOGY SIDDHARTH VENKATESH Abstract. solar wishing wellWebbEvery simplicial sheaf is a simplicial presheaf, and the inclusion functor sShv(C) ⊂sPre(C) has a left adjoint L2: sPre(C) →sShv(C) which is deﬁned by putting in the appropriate … solar wire size guide