Examples
The rich set of examples is given by adjunctions (see Monads and adjunctions), and the free group example mentioned above belongs to that set. Another example, on the category : for a set let be the power set of and for a function let be the function between the power sets induced by taking direct images under . For every set, we have a map, which assigns to every the singleton . The function
in fact is union (arbitrary union, not finitary union). These data describe a monad.
Closure operators are monads on preorder categories.
Read more about this topic: Monad (category Theory)
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