Theorem 5.35

Let $A$, $B$ be 5.1 Sets and let $f:A\to B$ be a function. Then the following are equivalent,

1. $f$ in invertible
2. $f$ is bijective
3. There exists a function $g:B\to A$ with $(g\circ f)={\iota }_A$ and $(f\circ g)={\iota }_B$