👉 In mathematics, a precanonical object is an object that can be realized as a sheaf on a scheme. A sheaf is a mathematical structure such that it assigns to each open set in a topological space its values, which are usually functions. Precanonical objects have the property of being locally free, meaning that they are locally generated as sheaves over the base space. In the context of algebraic geometry and schemes, precanonical objects are particularly important because they provide a way to define the