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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 (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 ...
The sliding filament theory Diagrammatic explanation of sliding filament hypothesis. The sliding filament theory was born from two consecutive papers published on the 22 May 1954 issue of Nature under the common theme "Structural Changes in Muscle During Contraction". Though their conclusions were fundamentally similar, their underlying ...
Actin cytoskeleton of mouse embryo fibroblasts, stained with Fluorescein isothiocyanate - phalloidin. Microfilaments, also called actin filaments, are protein filaments in the cytoplasm of eukaryotic cells that form part of the cytoskeleton. They are primarily composed of polymers of actin, but are modified by and interact with numerous other ...
Sloan Great Wall (SDSS Great Wall) 2003. z=0.07804. 433 Mpc long. This was the largest known galaxy filament to be discovered, [22] until it was eclipsed by the Hercules–Corona Borealis Great Wall found ten years later. Sculptor Wall (Southern Great Wall, Great Southern Wall, Southern Wall) 8000 km/s long.
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 ...
Sebaceous filaments are natural, healthy features that help move sebum to the skin’s surface for moisturizing. Blackheads form when too much sebum, dead skin cells, and bacteria clog a pore ...
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