The Cotangent Bundle (Natural Transformations)

11.8 Suppose C and D are categories, and \mathscr{F}, \mathscr{G} are (covariant or contravariant) functors from C to D. A natural transformation \gamma from \mathscr{F} to \mathscr{G} is a rule that assigns to each object X \in Ob(C) a morphism \lambda_{X} \in Hom_{D}(\mathscr{F}(X), \mathscr{G}(X)) in such a way that for every pair of objects X, Y \in Ob(C) and every morphism f \in Hom_{C}(X,Y), the following diagram commutes…

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