Category theory; homological algebra Additive and abelian categories Concept
Additive functor
Summary
An additive functor is a functor between preadditive categories that respects the addition of morphisms. Between additive categories, these are exactly the functors that preserve finite biproducts. Hom functors, tensor products with a fixed module and derived functors are additive. Additivity is the basic compatibility needed to apply a functor to chain complexes and exact sequences.
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About this page
| Tag | KAN07YC9T2 |
|---|---|
| URI | m2://KAN07YC9T2 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18E05 |
| Specializes | Functor |
| Changed | 2 November 2026 |
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Used by
- Exact functor
- Triangulated category
- Derived functor
- Delta functor
- Acyclic object
- Octahedral axiom
- Grothendieck spectral sequence