Category theory; homological algebra Limits and colimits Concept
Coproduct
Summary
The coproduct of a family of objects in a category is an object with an injection from each member of the family. Any family of morphisms out of the members factors uniquely through it. It is the notion dual to the product, and it is the colimit of a diagram with no non-identity arrows. It is the disjoint union for sets and topological spaces, the direct sum for abelian groups and modules, and the free product for groups.
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About this page
| Tag | 4FJ0S71P58 |
|---|---|
| URI | m2://4FJ0S71P58 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18A30 |
| Specializes | Colimit |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Biproduct
- Giraud's theorem
- Extensive category
- Galois category
- Brown representability theorem
- Small object argument