In detail, a $1$-morphism $f\colon A\to B$ of $\mathcal{C}$ is pseudomonic if it satisfies the following conditions:
-
For all diagrams in $\mathcal{C}$ of the form
if we have
\[ \text{id}_{f}\mathbin {\star }\alpha =\text{id}_{f}\mathbin {\star }\beta , \]then $\alpha =\beta $.
-
For each $X\in \text{Obj}\webleft (\mathcal{C}\webright )$ and each $2$-isomorphism of $\mathcal{C}$, there exists a $2$-isomorphism
of $\mathcal{C}$ such that we have an equality
of pasting diagrams in $\mathcal{C}$, i.e. such that we have
\[ \beta =\text{id}_{f}\mathbin {\star }\alpha . \]
