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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In category theory, a strong monad over a monoidal category (C,otimes,I) is a monad (T, , ) together with a natural transformation t_{A,B} : Aotimes TBto T(Aotimes B), called (tensorial) strength, such that the diagrams. In category theory, a monad or triple is an (endo-)functor, together with two associated natural transformations. Monads are important in the theory of pairs of adjoint functors, and they generalize closure operators on partially ordered sets to arbitrary categories. The notion of "algebras for a monad" generalizes classical notions from universal algebra, and in this sense, monads can be thought of as "theories".