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In mathematics, especially in sheaf theory—a domain applied in areas such as topology, logic and algebraic geometry—there are four image functors for sheaves that belong together in various senses.
Given a continuous mapping f: X → Y of topological spaces, and the category Sh of sheaves of abelian groups on a topological space. The functors in question are
The exclamation mark is often pronounced "shriek" , and the maps called "f shriek" or "f lower shriek" and "f upper shriek"—see also shriek map.
The exceptional inverse image is in general defined on the level of derived categories only. Similar considerations apply to étale sheaves on schemes.
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