Implication Details

Claim: If a functor is pseudomonic, then it is conservative.

Proof: Let $F$ be a pseudomonic functor and let $f$ be a morphism in its domain such that $F(f)$ is an isomorphism. Then $F(f)^{-1} = F(g)$ for some isomorphism $g$ since $F$ is full on isomorphisms. Then $f \circ g$ and $g \circ f$ are identities since $F$ is faithful and their images are identities.