representable functor

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representable functor teriminin İngilizce İngilizce sözlükte anlamı

Given a category C, a covariant representable functor hA sends each object X in category C to C(A,X), the set of arrows from A to X, and sends each arrow f: X → Y to a function from C(A,X) to C(A,Y) which maps each element s of C(A,X) to an element f \circ s of C(A,Y). A contravariant representable functor hA sends each object X in category C to set C(X,A) and each arrow f: X → Y to a function from C(Y,A) to C(X,A) which maps each element s of C(Y,A) to an element s\circ f of C(X,A). Note: hA: C → Sets and hA: Cop → Sets, because hA reverses the direction of the morphisms, whereas hA does not

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representable func·tor