Shriek map

In category theory, a branch of mathematics, certain unusual functors are denoted ${\displaystyle f_{!}}$ and ${\displaystyle f^{!},}$ with the exclamation mark used to indicate that they are exceptional in some way. They are thus accordingly sometimes called shriek maps, with "shriek" being slang for an exclamation mark, though other terms are used, depending on context.

Shriek notation is used in two senses:

In algebraic geometry, these arise in image functors for sheaves, particularly Verdier duality, where ${\displaystyle f_{!}}$ is a "less usual" functor.

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