What does pullback mean?

Definitions for pullback
ˈpʊlˌbækpull·back

This dictionary definitions page includes all the possible meanings, example usage and translations of the word pullback.

Princeton's WordNet

  1. pullback, tiebacknoun

    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"

  2. pullbacknoun

    (military) the act of pulling back (especially an orderly withdrawal of troops)

    "the pullback is expected to be over 25,000 troops"

Wiktionary

  1. pullbacknoun

    The act or result of pulling back; a withdrawal

  2. pullbacknoun

    That which holds back, or causes to recede; a drawback; a hindrance.

  3. pullbacknoun

    The iron hook fixed to a casement to pull it shut, or to hold it partly open at a fixed point.

  4. pullbacknoun

    A reduction in the price of a financial instrument after reaching a peak

  5. pullbacknoun

    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 .

Wikipedia

  1. Pullback

    In mathematics, a pullback is either of two different, but related processes: precomposition and fiber-product. Its dual is a pushforward.

ChatGPT

  1. pullback

    In mathematics, a pullback is a concept in category theory that captures the intuition of limiting or restricting morphisms to a smaller domain. It refers to the limit of a diagram consisting of two morphisms with a common codomain. A pullback is essentially the most general solution to the problem of finding an object in a category that maps to two given objects under two specified morphisms. Formally, given a category C, and a pair of morphisms f: X → Z and g: Y → Z in C, a pullback of the pair (f, g) is an object P along with two morphisms p1: P → X and p2: P → Y such that the following conditions hold: 1. f o p1 = g o p2 (where "o" denotes composition) 2. For any object Q and pair of morphisms q1: Q → X and q2: Q → Y with f o q1 = g o q2, there exists a unique morphism q: Q → P such that p1 o q = q1 and p2 o q = q2. This second condition exemplifies the universal property of the pullback. That is, the pullback P along with the morphisms p1 and p2 provides the "best" solution in terms of morphisms to the pair (f, g). The pullback, when it exists, is unique up to a unique isomorphism. Pullbacks are important in various areas of mathematics including algebraic geometry, group theory, topology, and homological algebra.

Webster Dictionary

  1. Pullbacknoun

    that which holds back, or causes to recede; a drawback; a hindrance

  2. Pullbacknoun

    the iron hook fixed to a casement to pull it shut, or to hold it party open at a fixed point

Wikidata

  1. 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.

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Numerology

  1. Chaldean Numerology

    The numerical value of pullback in Chaldean Numerology is: 1

  2. Pythagorean Numerology

    The numerical value of pullback in Pythagorean Numerology is: 6

Examples of pullback in a Sentence

  1. James Mattis:

    Thirty days from now we want to see everybody around a peace table based on a ceasefire, based on a pullback from the border and then based on ceasing dropping of bombs that will permit the( United Nations-sponsored) special envoy, Martin Griffiths -- he's very good, Martin Griffiths knows what Martin Griffiths's doing -- to get them together in Sweden and end this war.

  2. Stephen Massocca:

    It wasn't going to take much to prompt the decline, it's probably more resting than anything else. We've had a pretty significant move higher, we've marched straight up from 1,970 or so to about 2,100 so it's only natural that we are going to get a little bit of a pullback here.

  3. Cliff Hodge:

    We've been in the camp that we're overdue for a correction, something in the 5-10 % range that is a buyable pullback and we seem to be getting that now.

  4. Youssef Zohny:

    The resource areas of the market have been extremely strong this year and likely are going to see a pullback here given they look pretty stretched and likely overbought.

  5. Manik Narain:

    EM fixed income benchmarks are giving double digit returns so there is a lot of appetite out there to chase those returns higher still, post-BOJ there is a small pullback but it's concentrated on oil-centred emerging markets and the market seems confident the low-yield environment and stabilising emerging growth is consistent with EM assets holding up.

Popularity rank by frequency of use

pullback#10000#81228#100000

Translations for pullback

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"pullback." Definitions.net. STANDS4 LLC, 2024. Web. 8 Jun 2024. <https://www.definitions.net/definition/pullback>.

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