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Another example of a pullback comes from the theory of fiber bundles: given a bundle map π : E → B and a continuous map f : X → B, the pullback (formed in the category of topological spaces with continuous maps) X × B E is a fiber bundle over X called the pullback bundle. The associated commutative diagram is a morphism of fiber bundles.
When =, then the pullback and the pushforward describe the transformation properties of a tensor on the manifold . In traditional terms, the pullback describes the transformation properties of the covariant indices of a tensor; by contrast, the transformation of the contravariant indices is given by a pushforward.
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 ...
A typical example of a funnel chart starts with the sales leads on top, then down to the qualified leads, the hot leads and the closed deals. A business is bound to lose some number of potential deals at each step in the sales process and this is represented by the narrowing sections as you move from the top section (the widest) to the bottom section (the narrowest.)
It’s finally here: the long-predicted consumer pullback. Starbucks announced a surprise drop in same-store sales for its latest quarter, sending its shares down 17% on Wednesday. Pizza Hut and ...
The limit of this diagram is called the J th power of X and denoted X J. Equalizers. If J is a category with two objects and two parallel morphisms from one object to the other, then a diagram of shape J is a pair of parallel morphisms in C. The limit L of such a diagram is called an equalizer of those morphisms. Kernels.
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 over f(b′).
Marketing funnel encompasses several strategic approaches designed to engage customers at different stages of the buying and fidelization process. Each subset within the marketing funnel has specific objectives and targets particular interactions with customers, from initial contact to post-purchase follow-up.