Definition:Inverse Morphism

Definition
Let $\mathbf C$ be a metacategory.

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

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


 * $g \circ f = \operatorname{id}_X$
 * $f \circ g = \operatorname{id}_Y$

where $\operatorname{id}_X$ denotes the identity morphism on $X$.

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

Also see

 * Inverse Morphism is Unique
 * Isomorphism