---- > [!definition] Definition. ([[forgetful functor]]) > Let $\mathsf{C}$, $\mathsf{D}$ be [[category|categories]]. Informally, a **forgetful functor** $\mathsf{C} \to \mathsf{D}$ is a [[covariant functor|functor]] that 'drops' some of the structure from $\mathsf{C}$ to 'turn it into $\mathsf{D}. For example, a forgetful functor $\mathsf{Grp} \to \mathsf{Set}$ views each group as its underlying set and each group homomorphism as its underlying set-function, 'forgetting' about the multiplication. Other examples include $\mathsf{Top} \to \mathsf{Set}$, $\mathsf{Ring} \to \mathsf{Ab}$, $\mathsf{Met} \to \mathsf{Top}$, $\mathsf{TopGrp} \to \mathsf{Top}$, $\mathsf{TopGrp} \to \mathsf{Grp}$, $\dots$. ^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 > ```