Presheaf (category theory, $X:{\mathcal{C}}^{\mathrm{op}}\to \mathbf{Set}$)

In category theory, a presheaf is a structure that assigns data to the open sets of a topological space (or more generally, to objects in a category) in a way that respects the relationships between these sets (or objects). More formally, a presheaf can be defined as follows: ### Definition: Let \( C \) be a category and \( X \) a topological space (or a more abstract site).