# 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…

This site uses Akismet to reduce spam. Learn how your comment data is processed.