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monad [2015/02/17 18:48] nikolaj |
monad [2015/10/05 16:23] nikolaj |
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| | @#55EE55: postulate | @#55EE55: $\mu\circ T\eta=\mu\circ\eta T=1_T$ | | | @#55EE55: postulate | @#55EE55: $\mu\circ T\eta=\mu\circ\eta T=1_T$ | | ||
| - | ==== Discussion ==== | + | ----- |
| - | === Idea === | + | === Discussion === |
| A monad is functor together with two natural transformations that fulfill some algebraic relations. | A monad is functor together with two natural transformations that fulfill some algebraic relations. | ||
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| $\mu:TT\xrightarrow{\bullet}T$ | $\mu:TT\xrightarrow{\bullet}T$ | ||
| - | an is also a monoid object, namely in the category of endofunctors ${\bf C}^{\bf C}$, with the monoidal product $\otimes$ (not the categorical product) given by concatenation of functors $S\otimes T:= ST$. | + | and is also a monoid object, namely in the category of endofunctors ${\bf C}^{\bf C}$, with the monoidal product $\otimes$ (not the categorical product) given by concatenation of functors $S\otimes T:= ST$. |
| === Reference === | === Reference === | ||
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| [[http://en.wikipedia.org/wiki/Monad_%28category_theory%29|Monad (category theory)]], | [[http://en.wikipedia.org/wiki/Monad_%28category_theory%29|Monad (category theory)]], | ||
| [[http://de.wikipedia.org/wiki/Monade_%28Informatik%29|Monade (Informatik)]] | [[http://de.wikipedia.org/wiki/Monade_%28Informatik%29|Monade (Informatik)]] | ||
| - | ==== Parents ==== | + | |
| + | ----- | ||
| === Context === | === Context === | ||
| === Requirements === | === Requirements === | ||
