---- > [!definition] Definition. ([[essentially surjective functor]]) > Let $\mathsf{C}$ and $\mathsf{D}$ be [[category|categories]]. A [[covariant functor|functor]] $\mathscr{F}:\mathsf{C} \to \mathsf{D}$ is said to be **essentially surjective** if every object in $\mathsf{D}$ is [[isomorphism|isomorphic]] to an object $\mathscr{F}(C)$ for some $C$ in $\text{Obj}(\mathsf{C})$. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```