A functor $F\colon \mathcal{C}\to \mathcal{D}$ is pseudoepic if it satisfies the following conditions:
-
1.
For all diagrams of the form
if we have
\[ \alpha \mathbin {\star }\operatorname {\mathrm{id}}_{F}=\beta \mathbin {\star }\operatorname {\mathrm{id}}_{F}, \]then $\alpha =\beta $.
-
2.
For each $X\in \operatorname {\mathrm{Obj}}\webleft (\mathcal{C}\webright )$ 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
\[ \beta =\alpha \mathbin {\star }\operatorname {\mathrm{id}}_{F}. \]
