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Additive functor
Definition
Let and be preadditive categories (Preadditive category). A functor (Covariant functor, identity functor, composite functor, and contravariant functor) is additive when for every pair of objects the induced map
is a homomorphism of abelian groups. Equivalently,
for all parallel morphisms .
Depends on
Used by
- Additive functors and natural transformations form a preadditive category Proposition
- An additive functor preserves zero morphisms Proposition
- An additive functor preserves finite biproducts Theorem
- The idempotent completion is idempotent complete and its inclusion is fully faithful and universal Theorem
Dependency tree · two levels
4 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- The Stacks Project, Section 12.7, Additive functors (standard reference, not scraped)