---- > [!definition] Definition. ([[bifunctor]]) > Let $\mathsf{C}$, $\mathsf{D}$, $\mathsf{E}$ be [[category|categories]]. A **bifunctor** $\mathscr{F}:\mathsf{C} \times \mathsf{D} \to \mathsf{E}$ is a [[covariant functor|functor]] whose domain is the [[product category]] $\mathsf{C} \times \mathsf{D}$. ^definition > [!basicexample] > Sometimes one wants a bifunctor that is [[contravariant functor|contravariant]] in the first variable and [[covariant functor|covariant]] in the second, for example $\text{Hom}_{\mathsf{C}}(-,-):\mathsf{C}^{\text{op}} \times \mathsf{C} \to \mathsf{Set}.$ ^basic-example ---- #### ---- #### 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 > ```