Shriek Map
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High Quality Content by WIKIPEDIA articles! In category theory, a branch of mathematics, certain unusual functors are denoted f! and 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. In algebraic geometry, these arise in image functors for sheaves, particularly Verdier duality, where f! is a "less usual" functor. In algebraic topology, these arise particularly in fiber bundles, where they yield maps…mehr

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High Quality Content by WIKIPEDIA articles! In category theory, a branch of mathematics, certain unusual functors are denoted f! and 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. In algebraic geometry, these arise in image functors for sheaves, particularly Verdier duality, where f! is a "less usual" functor. In algebraic topology, these arise particularly in fiber bundles, where they yield maps that have the opposite of the usual variance. They are thus called wrong way maps, Gysin maps, as they originated in the Gysin sequence, or transfer maps. A fiber bundle F to E to B, with base space B, fiber F, and total space E, has, like any other continuous map of topological spaces, a covariant map on homology H_ (E) to H_ (B) and a contravariant map on cohomology H^ (B) to H^ (E).