Monad (category theory)

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In category theory, a branch of mathematics, a monad is a triple ( T , η , μ ) {\displaystyle (T,\eta ,\mu )} consisting of a functor T from a category to itself and two natural transformations η , μ {\displaystyle \eta ,\mu } that satisfy versions of the associativity and unitality axioms. Equivalently, a monad is a monoid in the category of endofunctors of some fixed category (an endofunctor is a functor mapping a category to itself). For example, if F , G {\displaystyle F,G} are functors adjoint to each other, then T = G ∘ F {\displaystyle T=G\circ F} together with η , μ {\displaystyle \eta ,\mu } determined by the adjoint relation is a monad...

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