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