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The functoriality of C C is the property that C C "plays nicely" with this categorial structure: roughly speaking, given a group homomorphism f: A → B f: A → B, I should get a continuous map cf: C(A) → C(B) c f: C ( A) → C ( B) in some reasonable way. 725 Algebraic Geometry I Lecture Lecture 11: Sheaf Functors and Quasi-coherent Sheaves Recall that last time we de ned a sheaf and a presheaf on a topological space, respectively denoted as2 Answers. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Welcome to our comprehensive review of Funcrot. It is simply to show that often, you instantiate the functor "on the fly", when you. Let mathcal {C} and mathcal {D} be sites. A functor F from C to D is a mapping that [3] F ( i d X ) = i d F ( X ) {displaystyle F (mathrm {id} _ {X})=mathrm {id} _ {F (X)},!} f : X → Y {displaystyle. One of them is: the skeleta of the two categories are isomorphic categories. 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