Category theory; homological algebra Limits and colimits Concept
Colimit
Summary
The colimit of a diagram in a category is a universal cocone under it. It maps to every other cocone in exactly one compatible way. It is the notion dual to a limit, and it covers coproducts, coequalizers, pushouts, direct limits and initial objects. Colimits glue objects together, while limits cut out compatible families.
Where this leads
15 pages build on this one.
Further reading
About this page
| Tag | BJS1CGTKQ5 |
|---|---|
| URI | m2://BJS1CGTKQ5 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18A30 |
| Changed | 2 November 2026 |
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Used by
- Grothendieck category
- Ind-completion
- Final functor
- Density theorem
- Filtered colimits commute with finite limits
- Sketch
- Pointwise Kan extension formula
- Coequalizer
- Model category
- Locally presentable category
- Accessible category
- Direct limit
- Small object argument
- Coproduct
- Pushout