Monad (Category Theory)
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A Monad (Category Theory) is a Category Theory that ...
- AKA: Monad (Category Theory).
- See: Category Theory, Functor, Natural Transformation, Adjoint Functors, Closure Operator, Partially Ordered Set, Saunders Mac Lane, Monad (Philosophy).
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/monad_(category_theory) Retrieved:2014-4-24.
- In category theory, a branch of mathematics, a monad, or triple is an (endo-)functor, together with two natural transformations. Monads are used in the theory of pairs of adjoint functors, and they generalize closure operators on partially ordered sets to arbitrary categories. Saunders Mac Lane adopted the philosophical term "monad" (a single entity that generates all other entities) for this construct, noting the construct's ability to generate a corresponding category. [1]
- ↑ Mac Lane, Saunders (1998) Categories for the Working Mathematician: "The remarkable part is that the whole category Algτ can be reconstructed from this monad in Set.”