- 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...
- 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...
-
coproduct mapping to A, and a
morphism A' → A, the
pullback is an I-indexed
coproduct of the
pullbacks: ( ∐ i ∈ I B i ) × A A ′ ≅ ∐ i ∈ I ( B i × A A ′...
-
forms along with the
exterior derivative defined on it is
preserved by the
pullback under smooth functions between two manifolds. This
feature allows geometrically...
