Information om | Engelska ordet COLIMITS

Exempel på hur man kan använda COLIMITS i en mening

• This means that P is projective if and only if this functor preserves epimorphisms (surjective homomorphisms), or if it preserves finite colimits.
• A covariant (not necessarily additive) functor is left exact if and only if it turns finite limits into limits; a covariant functor is right exact if and only if it turns finite colimits into colimits; a contravariant functor is left exact iff it turns finite colimits into limits; a contravariant functor is right exact iff it turns finite limits into colimits.
• One can use the mapping cylinder to construct homotopy colimits: this follows from the general statement that any category with all pushouts and coequalizers has all colimits.
• Tillotson have shown that Seq is the smallest Cartesian closed subcategory of Top containing the underlying topological spaces of all metric spaces, CW-complexes, and differentiable manifolds and that is closed under colimits, quotients, and other "certain reasonable identities" that Norman Steenrod described as "convenient".
• Like many other algebraic categories, the forgetful functor U : Ring → Set creates (and preserves) limits and filtered colimits, but does not preserve either coproducts or coequalizers.
• Then, one uses a presentation of filtered colimits as a coequalizer (which is a finite colimit) of an infinite coproduct.
• The category Meas is both complete and cocomplete, which means that all small limits and colimits exist in Meas.

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