An endomorphism $f$ such that $f\circ f=1$

Question

What is the name for an endomorphism $f$ of a category such that $f\circ f=1$?

Note that I work with category $\mathbf{Set}$.

Answer 1

A mapping $f:X\to X$, for a set $X$, which satisfy $f\circ f=1$ is called involution.