Category theory; homological algebra Limits and colimits Concept
Limit
Summary
The limit of a diagram in a category is a universal cone over it. Every other cone factors through it in exactly one way. Limits unify many constructions, such as products, equalizers, pullbacks, inverse limits and terminal objects. A limit is unique up to unique isomorphism when it exists, and in the category of sets every small diagram has one.
Where this leads
16 pages build on this one.
- Product
- Equalizer
- Homotopy limit
- Filtered colimits commute with finite limits
- Complete category
- Sketch
- Pointwise Kan extension formula
- Existence of limits from products and equalizers
- Pullback
- Pro-object
- Preservation of limits
- Model category
- Finitely complete category
- Right adjoints preserve limits
- Inverse limit
- Colimit
Further reading
About this page
| Tag | CHS5AFJGWE |
|---|---|
| URI | m2://CHS5AFJGWE |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18A30 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Product
- Equalizer
- Homotopy limit
- Filtered colimits commute with finite limits
- Complete category
- Sketch
- Pointwise Kan extension formula
- Existence of limits from products and equalizers
- Pullback
- Pro-object
- Preservation of limits
- Model category
- Finitely complete category
- Right adjoints preserve limits
- Inverse limit
- Colimit