Category:Examples of Isomorphisms of Categories

This category contains examples of Isomorphism of Categories.

Let $\mathbf C$ and $\mathbf D$ be metacategories.

Let $F: \mathbf C \to \mathbf D$ be a functor.

Then $F$ is an isomorphism (of categories) if and only if there exists a functor $G: \mathbf C \to \mathbf D$ such that:

$G F: \mathbf C \to \mathbf C$ is the identity functor $I_{\mathbf C}$

$F G: \mathbf D \to \mathbf D$ is the identity functor $I_{\mathbf D}$