David Roberts pseudoinverse

In a bicategory $B$ a pseudoinverse to a 1-arrow $f:x \to y$ is a 1-arrow $g:y \to x$ such that there are invertible 2-cells $a:fg \Rightarrow id$, $b:gf \Rightarrow id$. Clearly a pseudoinverse exists if and only if $f$ is an equivalence.