Definition 5.50.
For an acyclic class \(L\), we define
\[L^{\mathrm{epi}} := L \cap \EffEpi,
\qquad \qquadtext{ and } \qquad
L^{\mathrm{mono}} := (L \cap \Mono)^{m} = (L \cap \Mono)^{c},\]
where the last equality holds by Corollary 5.43. We say \(L\) is monogenic if \(L = L^{\mathrm{mono}}\) (i.e. generated by its monomorphisms), and epigenic if \(L = L^{\mathrm{epi}}\) (i.e. it is contained in the effective epimorphisms).