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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Distributive law between monads ： ウィキペディア英語版 Distributive law between monads In category theory, an abstract branch of mathematics, distributive laws between monads are a way to express abstractly that two algebraic structures distribute one over the other one. Suppose that $(S,\backslash mu^S,\backslash eta^S)$ and $(T,\backslash mu^T,\backslash eta^T)$ are two monads on a category C. In general, there is no natural monad structure on the composite functor ''ST''. On the other hand, there is a natural monad structure on the functor ''ST'' if there is a distributive law of the monad ''S'' over the monad ''T''. Formally, a distributive law of the monad ''S'' over the monad ''T'' is a natural transformation :$l:TS\backslash to\; ST$ such that the diagrams :          :          commute. This law induces a composite monad ''ST'' with * as multiplication: $STST\backslash xrightarrowSSTT\backslash xrightarrowST$, * as unit: $1\backslash xrightarrowST$. == See also == * distributive law 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Distributive law between monads」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.