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Exact functor

In mathematics, particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for algebraic calculations because they can be directly applied to presentations of objects. Much of the work in homological algebra is designed to cope with functors that fail to be exact, but in ways that…

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Exact functor

Nodes53
Edges52
Triples15
Avg. degree1.96
Density0.037736
Components1

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Exact functor

Top relations

related to Examples · 7
Exact functor → Ab, Every, FA, GA, Hom, HomA, The
related to Generalizations · 5
Exact functor → Despite, For, Grothendieck, In SGA4, The
related to Definitions · 2
Exact functor → Let, We
is a · 1
Exact functor → functor that preserves short exact sequences

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Important terminology

exact displaystyle functor otimes functors sequence left abelian short right mathbf category injective left-exact r-modules cong 12 covariant turns tensor

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Exact functoris afunctor that preserves short exact sequences0.90text
Exact functorrelated to DefinitionsLet0.60section
Exact functorrelated to DefinitionsWe0.60section
Exact functorrelated to ExamplesEvery0.60section
Exact functorrelated to ExamplesThe0.60section
Exact functorrelated to ExamplesHom0.60section
Exact functorrelated to ExamplesFA0.60section
Exact functorrelated to ExamplesHomA0.60section
Exact functorrelated to ExamplesAb0.60section
Exact functorrelated to ExamplesGA0.60section
Exact functorrelated to GeneralizationsIn SGA40.60section
Exact functorrelated to GeneralizationsThe0.60section

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