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

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

space of 1-forms on M {\displaystyle M} . This linear map is known as the pullback (by ϕ {\displaystyle \phi } ), and is frequently denoted by ϕ ∗ {\displaystyle...

In mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle π : E → B and...

A pullback motor (also pull back, pull back and go or pull-back) is a simple clockwork motor used in toy cars. A patent for them was granted to Bertrand...

given a continuous map f: X → Y of topological spaces and a ring R, the pullback along f on cohomology theory is a grade-preserving R-algebra homomorphism:...

non-autonomous. This requires one to consider the notion of a pullback attractor or attractor in the pullback sense. Consider a random dynamical system φ {\displaystyle...

forms along with the exterior derivative defined on it is preserved by the pullback under smooth functions between two manifolds. This feature allows geometrically...

possibly coming to an end. For the decade, the Dow saw a rather substantial pullback for a negative return from 11,497.12 to 10,428.05, a loss of a 9.3%. During...

{\displaystyle f\colon X\to Y} . We will call the result the inverse image or pullback sheaf f − 1 G {\displaystyle f^{-1}{\mathcal {G}}} . If we try to imitate...

of modules#Operations). The pullback of a vector bundle is a vector bundle of the same rank. In particular, the pullback of a line bundle is a line bundle...

categories. A morphism is a monomorphism if it is idempotent with respect to pullbacks. The categorical dual of a monomorphism is an epimorphism, that is, a...

{\displaystyle P=X+_{Z}Y} . The pushout is the categorical dual of the pullback. Explicitly, the pushout of the morphisms f and g consists of an object...

f_{*}^{}\colon T_{x}M\to T_{f(x)}N} every such map induces a linear map (called the pullback) between the cotangent spaces, only this time in the reverse direction:...

Radon–Nikodym derivatives of both the pullback and pushforward measures of m {\displaystyle m} under T {\displaystyle T} . The pullback measure in terms of a transformation...

A homotopy pullback (or homotopy fiber-product) is the dual concept of a homotopy pushout.It satisfies the universal property of a pullback up to homotopy...

morphism A ′ → A {\displaystyle A'\to A} , the pullback is an I {\displaystyle I} -indexed coproduct of the pullbacks: ( ∐ i ∈ I B i ) × A A ′ ≅ ∐ i ∈ I ( B i...

step, shuffle, leap, toe. The Maxie Ford is famous for its use of the pullback (or graboff) after the shuffle and best known as the Maxie Ford Break:...

Choro-Q is a line of Japanese 3–4 cm pullback car toys produced by Takara Tomy (formerly Takara). Known in North America as Penny Racers, they were introduced...

Bust-a-Move DS, known as Pullback!! Puzzle Bobble (Japanese: ひっぱって!!パズルボブル, Hepburn: Hippatte!! Pazuru Boburu) in Japan, is a puzzle video game developed...

most important one is the product of two smooth valuations. Together with pullback and pushforward, this operation extends to valuations on manifolds. Let...

and for all arrows f:c″→c′, S(f) is the restriction of Hom(f, c), the pullback by f (in the sense of precomposition, not of fiber products), to S(c′);...

In mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology...

the essential properties of universal constructions such as products, pullbacks and inverse limits. The dual notion of a colimit generalizes constructions...

{\displaystyle d\varphi _{x}} is invertible, and the inverse gives the pullback of T φ ( x ) N . {\displaystyle T_{\varphi (x)}N.} The differential is...

} {\displaystyle f^{*}(E)=\{(a,e)\in A\times E\ |\ f(a)=p(e)\}} is the pullback and the projections of f ∗ ( E ) {\displaystyle f^{*}(E)} onto A {\displaystyle...

many applications. At a basic level, this has to do with functions and pullbacks in geometric situations: given spaces X {\displaystyle X} and Y {\displaystyle...

(also called a Doolittle diagram) is a diagram that is simultaneously a pullback square and a pushout square. It is a self-dual concept. Adámek, Jiří, Herrlich...

Gibbons, Robert (28 December 2011). "Oil falls on dollar's rise, Wall Street pullback". Reuters. Archived from the original on 8 January 2012. Retrieved 8 January...

the close. This was repeated the next trading day before another major pullback for the year. It took until Monday, June 4, 2018 (nearly three months)...