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{F}}} called the sheafification or sheaf associated to the presheaf F {\displaystyle {\mathcal {F}}} . For example, the sheafification of the constant...

{\displaystyle {\mathcal {F}}} , there is a standard device called sheafification or sheaving. The rough intuition of what one should do, at least for...

approximating them by a sequence of simpler functors; it generalizes the sheafification of a presheaf. This sequence of approximations is formally similar to...

A\to A} . The constant sheaf associated to A {\displaystyle A} is the sheafification of the constant presheaf associated to A {\displaystyle A} . This sheaf...

, resp. F e t {\displaystyle F_{et}} , denotes the h-sheafification, resp. etale sheafification. As mentioned above, in positive characteristic, any h-sheaf...

{\mathcal {F}}} on X, let F + {\displaystyle {\mathcal {F}}^{+}} denote its sheafification. Then we have a natural comparison map χ : H ˇ ∗ ( X , F ) → H ∗ ( X...

used in a similar way to words like 'generalization', and not like 'sheafification'. One form of categorification takes a structure described in terms...

subcategory of presheaves on a topological space. The reflector is sheafification, which assigns to a presheaf the sheaf of sections of the bundle of...

tightly linked: Given a presheaf P {\displaystyle {\mathcal {P}}} and its sheafification F = P + {\displaystyle {\mathcal {F}}={\mathcal {P}}^{+}} , the stalks...

does not define an algebraic group, or even an fppf sheaf, and its sheafification in the fppf topology is in fact PGL(n, K). PSL and PGL are centerless...

an S-scheme T to G(T)/H(T) is in general not a sheaf, and even its sheafification is in general not representable as a scheme. However, if H is finite...

) . {\displaystyle U\mapsto F(U)\otimes _{O(U)}G(U).} (To see that sheafification cannot be avoided, compute the global sections of O ( 1 ) ⊗ O ( − 1...

A} then we define the sheaf K n , A {\displaystyle K_{n,A}} as the sheafification of the following pre-sheafpg 4 K n , A p r e : U ↦ A t r ( A n ) ( U...

sheaf L | U {\displaystyle {\mathcal {L}}|_{U}} is isomorphic to the sheafification of some constant presheaf. [clarification needed] If X is path-connected...

cd ( X ) {\displaystyle {\tilde {G}}_{n}^{\,{\text{cd}}}(X)} is the sheafification of these groups with respect to the Nisnevich topology, there is a convergent...

direct image functor R p f ∗ ( F ) {\displaystyle R^{p}f_{*}(F)} is the sheafification of the presheaf U ↦ H q ( f − 1 ( U ) , F ) {\displaystyle U\mapsto...

{\mathfrak {C}}} , then the NNO in E {\displaystyle {\mathcal {E}}} is the sheafification of Γ N {\displaystyle \Gamma _{\mathbb {N} }} and may be shown to take...

{Sch} /\mathbb {k} } , its cotangent sheaf can be computed from the sheafification of the cotangent module on the underlying graded algebra. For example...

way to associate a stack to a given prestack. It is similar to the sheafification of a presheaf and is called stackification. The idea of the construction...