CatDat

Implication Details

Assumptions: conservative, full

Conclusions: essentially injective

Proof: The functor even lifts isomorphisms: If $F(A) \to F(B)$ is an isomorphism, then it is induced by a morphism $A \to B$ since $F$ is full. Moreover, $A \to B$ is an isomorphism since its $F$-image is an isomorphism and $F$ is conservative.