colimit

Speech parts

1. colimit - Noun

2. colimit - Verb

Meaning

colimit (plural colimits)

(category theory) The cocone of a diagram through which any other cocone of that same diagram can factor uniquely.

colimit (third-person singular simple present colimits, present participle colimiting, simple past and past participle colimited)

(transitive) To limit along with another material.

Examples

A category has colimits of type J if every diagram of type J has a colimit in C. A cocomplete category is one that has all small colimits. Source: Internet

Any colimit functor is left adjoint to a corresponding diagonal functor (provided the category has the type of colimits in question), and the unit of the adjunction provides the defining maps into the colimit object. Source: Internet

Dually, an initial object is a colimit of the empty diagram ∅ → C and can be thought of as an empty coproduct or categorical sum. Source: Internet

Dually, if a diagram F : J → C has a colimit in C, denoted colim F, there is a unique canonical isomorphism : which is natural in the variable N and respects the colimiting cones. Source: Internet

Dually, if every diagram of type J has a colimit in C (for J small) there exists a colimit functor : which assigns each diagram its colimit. Source: Internet

More examples Every limit and colimit provides an example for a simple natural transformation, as a cone (category theory) amounts to a natural transformation with the diagonal functor as domain. Source: Internet

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