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Monad (category theory)
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Monad (category theory)
In
category theory
, a branch of mathematics, a
monad
(also
triple
,
triad
,
standard construction
and
fundamental construction
) is an
endofunctor
(a functor mapping a category to itself), 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.
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