pullbackˈpʊlˌbæk
pullback (n)
English Definitions:
pullback, tieback (noun)
a device (as a decorative loop of cord or fabric) for holding or drawing something back
"the draperies were drawn to the sides by pullbacks"
pullback (noun)
(military) the act of pulling back (especially an orderly withdrawal of troops)
"the pullback is expected to be over 25,000 troops"
pullback (Noun)
The act or result of pulling back; a withdrawal
pullback (Noun)
That which holds back, or causes to recede; a drawback; a hindrance.
pullback (Noun)
The iron hook fixed to a casement to pull it shut, or to hold it partly open at a fixed point.
pullback (Noun)
A reduction in the price of a financial instrument after reaching a peak
pullback (Noun)
Given a pair of morphisms and with a common codomain, Z, their pullback is a pair of morphisms and as well as their common domain, P, such that the equation is satisfied, and for which there is the universal property that for any other object Q for which there are also morphisms , ; there is a unique morphism such that and .
Pullback
Suppose that φ:M→ N is a smooth map between smooth manifolds M and N; then there is an associated linear map from the space of 1-forms on N to the space of 1-forms on M. This linear map is known as the pullback, and is frequently denoted by φ*. More generally, any covariant tensor field – in particular any differential form – on N may be pulled back to M using φ. When the map φ is a diffeomorphism, then the pullback, together with the pushforward, can be used to transform any tensor field from N to M or vice-versa. In particular, if φ is a diffeomorphism between open subsets of Rn and Rn, viewed as a change of coordinates, then the pullback and pushforward describe the transformation properties of covariant and contravariant tensors used in more traditional approaches to the subject. The idea behind the pullback is essentially the notion of precomposition of one function with another. However, by combining this idea in several different contexts, quite elaborate pullback operations can be constructed. This article begins with the simplest operations, then uses them to construct more sophisticated ones. Roughly speaking, the pullback mechanism turns several constructions in differential geometry into contravariant functors.
Pullback
In mathematics, a pullback is either of two different, but related processes: precomposition and fiber-product. Its dual is a pushforward.
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"pullback." Kamus.net. STANDS4 LLC, 2024. Web. 20 Apr. 2024. <https://www.kamus.net/english/pullback>.
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