Information om | Engelska ordet COLIMIT

Exempel på hur man kan använda COLIMIT i en mening

• The dual notion of a colimit generalizes constructions such as disjoint unions, direct sums, coproducts, pushouts and direct limits.
• Pushout (category theory) (also called an amalgamated sum or a cocartesian square, fibered coproduct, or fibered sum), the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domainor pushout, leading to a fibered sum in category theory.
• In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain.
• Characterization as colimit: Dually, if X is cocomplete and C is small, then the coend can be described as the coequalizer in the diagram.
• More generally, the category of elements plays a key role in the proof that every weighted colimit can be expressed as an ordinary colimit, which is in turn necessary for the basic results in theory of pointwise left Kan extensions, and the characterization of the presheaf category as the free cocompletion of a category.
• The Verdier hypercovering theorem states that the abelian sheaf cohomology of an étale sheaf can be computed as a colimit of the cochain cohomologies over all hypercovers.
• In category theory, a branch of mathematics, the density theorem states that every presheaf of sets is a colimit of representable presheaves in a canonical way.
• Then, one uses a presentation of filtered colimits as a coequalizer (which is a finite colimit) of an infinite coproduct.

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