Definition:Inverse Morphism

Definition
Let $\mathbf C$ be a metacategory.

Let $f: C \to D$ be a morphism of $\mathbf C$.

A morphism $g: D \to C$ is said to be an inverse (morphism) for $f$ iff:


 * $g \circ f = \operatorname{id}_C$ and $f \circ g = \operatorname{id}_D$

where, for example, $\operatorname{id}_C$ denotes the identity morphism on $C$.

It follows that $f$ is an isomorphism iff it has an inverse morphism.

Also see

 * Inverse Morphism is Unique
 * Isomorphism