---- > [!definition] Definition. ([[constant presheaf]]) > Let $\mathsf{C}$ be a reasonable [[category]] and $S$ an object of $\mathsf{C}$. > Let $X$ be a [[topological space]], and $S$ a set. Taking $\underline{S}_{\text{pre}}(U):=S$ for all open $U \subset X$ and $\text{res}_{UV}:=\id_{S}$ gives a [[presheaf]] on $X$, called the **constant presheaf**. It is rarely a [[sheaf]]. ^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 > ```