The Clowder Project

¹

1. The functor $F$ is a epimorphism of categories.
2. For each morphism $f\colon A\to B$ of $\mathcal{D}$, we have a diagram
   
   in $\mathcal{D}$ satisfying the following conditions:
   1. We have $f=\alpha _{0}\circ \phi _{1}$.
   2. We have $f=\psi _{m}\circ \alpha _{2m}$.
   3. For each $0\leq i\leq 2m$, we have $\alpha _{i}\in \textup{Mor}\webleft (\mathrm{Im}\webleft (F\webright )\webright )$.