---- > [!definition] Definition. ([[presheaf cokernel]]) > Let $f:\mathcal{F} \to \mathcal{G}$ be a [[morphism of (pre)sheaves|morphism of presheaves]] valued in a [[category]] where [[cokernel of a module homomorphism|cokernel]] make sense. The **presheaf cokernel** of $f$, $\ker f$, is the [[presheaf]] specified by $(\text{coker } f)(U):=\text{coker } \big(f_{U}:\mathcal{F}(U) \to \mathcal{G}(U)\big)$. ^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 > ```