Search results
Results from the Health.Zone Content Network
Pullback (category theory) 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. The pullback is written.
Pullback bundle. In mathematics, a pullback bundle or induced bundle [1] [2] [3] is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle π : E → B and a continuous map f : B′ → B one can define a "pullback" of E by f as a bundle f*E over B′. The fiber of f*E over a point b′ in B′ is just the fiber of E ...
Pullback (differential geometry) Let be a smooth map between smooth manifolds and . Then there is an associated linear map from the space of 1-forms on (the linear space of sections of the cotangent bundle) to the space of 1-forms on . This linear map is known as the pullback (by ), and is frequently denoted by .
The pullback bundle is an example that bridges the notion of a pullback as precomposition, and the notion of a pullback as a Cartesian square. In that example, the base space of a fiber bundle is pulled back, in the sense of precomposition, above. The fibers then travel along with the points in the base space at which they are anchored: the ...
An operation of a different nature is the pullback bundle construction. Given a vector bundle E → Y and a continuous map f: X → Y one can "pull back" E to a vector bundle f*E over X. The fiber over a point x ∈ X is essentially just the fiber over f(x) ∈ Y.
The fiber over is the subspace = (). ... in the base space, is a fibration. Specifically it is the pullback fibration of the pathspace fibration ...
Universal bundle. In mathematics, the universal bundle in the theory of fiber bundles with structure group a given topological group G, is a specific bundle over a classifying space BG, such that every bundle with the given structure group G over M is a pullback by means of a continuous map M → BG .
22 high fiber foods to eat. Here are 22 healthy and satisfying high fiber foods. 1. Pears (3.1 grams) Pears are both tasty and nutritious and can satisfy a sweet tooth. They are also a good source ...