Webb$\begingroup$ I presume by stack you mean a fibred category (satisfying the usual properties), and by a sheaf of categories you mean a presheaf of categories satisfying the appropriate coherence (weaker than that for a sheaf of sets). The main problem is perhaps what you consider to be the 2-category of stacks, and what you want to take for 1 … WebbLet ℌ(Y(ɣ)) be a topological manifold homotopic to some space k \ k-1 such that a distinguished normalizable operator ⊔ f is generated by finite intersections and open covers on stalks of ℌ(Y(ɣ)). Define Y- r to be the fibered objects linking ℌ(*)

Definitions of a constant sheaf - Mathematics Stack Exchange

WebbThe sheaf spaceof A_{\displaystyle {\underline {A}}}is the projection map A{\displaystyle A}(where X×A→X{\displaystyle X\times A\to X}is given the discrete topology). A detailed … WebbGiven a presheaf F of abelian groups on X.Witheverypointx 2 F there is associated an abelian group Fxcalled the stalk (stilk) of F at x. The elements of Fx are called germs of sections (seksjonskimer eller bare kimer) near x. The definition goes as follows: We begin with the disjoint union ` brashear bedroom furniture

Constant sheaf - Wikipedia

Webb25 juni 2024 · Let F be a sheaf on a topological space. Of course, it is not true in general that F is entirely determined by its stalks, that is, there can be another sheaf G with F x ≃ … Webb0), each stalk is isomorphic to Z, that is, there is a non-canonical isomorphism H n(X;Xf x 0g;Z) ˘=Z for all x 0 2X. One veri es that the orientation sheaf o X is a locally constant sheaf whose stalks are isomorphic to Z. Moreover, if M is orientable, the sheaf o X is in fact the constant sheaf. For smooth WebbThe stalk of F at a point x ∈ X, denoted F x, is the group whose elements are equivalence classes of pairs (U,s) where U is a neighborhood of x and s ∈ F(U), ... Definition 8. A sub(pre)sheaf of F is a (pre)sheaf G such that G(U) ⊂ F(U) for every open set U, and whose restriction maps are the restrictions of the restriction maps of F. brashear bulls logo