Monad (linear algebra)

In linear and homological algebra, a monad is a 3-term complex

ABC

of objects in some abelian category whose middle term B is projective and whose first map A  B is injective and whose second map B  C is surjective. Equivalently a monad is a projective object together with a 3-step filtration (B ⊃ ker(B  C) ⊃ im(A  B)). In practice A, B, and C are often vector bundles over some space, and there are several minor extra conditions that some authors add to the definition. Monads were introduced by Horrocks (1964,p.698).

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