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The notion of pullback as a fiber-product ultimately leads to the very general idea of a categorical pullback, but it has important special cases: inverse image (and pullback) sheaves in algebraic geometry, and pullback bundles in algebraic topology and differential geometry. See also: Pullback (category theory) Fibred category; Inverse image sheaf
In mathematics, specifically in algebraic topology and algebraic geometry, an inverse image functor is a contravariant construction of sheaves; here “contravariant” in the sense given a map :, the inverse image functor is a functor from the category of sheaves on Y to the category of sheaves on X.
Exponential backoff is an algorithm that uses feedback to multiplicatively decrease the rate of some process, in order to gradually find an acceptable rate.
The pullback of bundles then corresponds to the inverse image of sheaves, which is a contravariant functor. A sheaf, however, is more naturally a covariant object, since it has a pushforward, called the direct image of a sheaf. The tension and interplay between bundles and sheaves, or inverse and direct image, can be advantageous in many areas ...
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a common codomain.
image impedance A parameter used in design of electrical networks such as filters. image noise reduction Any technique used to reduce interfering effects in processing of an image. image processing Electronic recording, storage, alteration and reproduction of pictures. impulse response The response of a network to a sudden narrow pulse input.
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(In the language of sheaves, pullback defines a morphism from the sheaf of smooth functions on to the direct image by of the sheaf of smooth functions on .) More generally, if f : N → A {\displaystyle f:N\to A} is a smooth map from N {\displaystyle N} to any other manifold A {\displaystyle A} , then ( ϕ ∗ f ) ( x ) = f ( ϕ ( x ...