Contents

category theory

# Contents

## Definition

The identity natural transformation on a functor $F: C \to D$ is the natural transformation $id_F: F \to F$ that maps each object $x$ of $C$ to the identity morphism $id_{F(x)}$ in $D$.

The identity natural transformations are themselves the identity morphisms for vertical composition of natural transformations in the functor category $D^C$ and in the 2-category Cat.

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