Monad (linear algebra)

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