Inverse image functor

In mathematics, the inverse image functor is a covariant construction of sheaves. The direct image functor is the primary operation on sheaves, with the simplest definition. The inverse image exhibits some relatively subtle features.

Suppose we are given a sheaf ${\displaystyle {\mathcal {G}}}$ on ${\displaystyle Y}$ and that we want to transport ${\displaystyle {\mathcal {G}}}$ to ${\displaystyle X}$ using a continuous map ${\displaystyle f\colon X\to Y}$.

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