CatDat

Implication Details

Assumptions: equivalence

Conclusions: left-invertible, right-invertible

This is an equivalence.

Proof: If a functor $F$ has a right inverse $R$ and a left inverse $L$, then $$L \cong L \circ F \circ R \cong R.$$ Hence, $R$ (and $L$) are (pseudo-)inverse to $F$.