A functor $F\colon \mathcal{C}\to \mathcal{D}$ is conservative if it satisfies the following condition:1
- For each $f\in \textup{Mor}\webleft (\mathcal{C}\webright )$, if $F\webleft (f\webright )$ is an isomorphism in $\mathcal{D}$, then $f$ is an isomorphism in $\mathcal{C}$.
1Slogan: A functor $F$ is conservative if it reflects isomorphisms.
