Category theory; homological algebra Additive and abelian categories Concept
Additive category
Summary
An additive category is a preadditive category with a zero object in which any two objects have a biproduct. Its morphisms between finite direct sums can be written as matrices of morphisms, composed by matrix multiplication. Categories of modules, of free modules and of vector bundles are additive. Additive categories are the natural home of chain complexes and of the homotopy category of chain complexes.
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| Tag | B2VP96NJSK |
|---|---|
| URI | m2://B2VP96NJSK |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18E05 |
| Specializes | Preadditive category |
| Same as |
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Definitions
Used by
- Abelian category
- Triangulated category
- Exact category
- Additive functor
- Homotopy category of chain complexes
- Chain map
- Octahedral axiom
- Chain complex
- Double complex
- Chain homotopy
- Mapping cone