Sheaf (mathematics)
Basic functoriality

Since the data of a (pre-)sheaf depends on the open subsets of the base space, sheaves on different topological spaces are unrelated to each other in the sense that there are no morphisms between them. However, given a continuous map f: X → Y {\displaystyle f:X\to Y} between two topological spaces, pushforward and pullback relate sheaves on X {\displaystyle X} to those on Y {\displaystyle Y} and vice versa.
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