The formal theory of monoidal monads

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• 作者：Marek Zawadowski ^{zawado@mimuw.edu.pl}
• 关键词：18C15 ; 18C20 ; 18D10 ; 18D05
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2012
• 期刊代码：35_00224049
• 类别：mt
• 出版时间：August, 2012
• 卷：216
• 期：8-9
• 页码：1932-1942
• 文件大小：228 K

摘要

We give a 3-categorical, purely formal argument explaining why on the category of Kleisli algebras for a lax monoidal monad, and dually on the category of Eilenberg-Moore algebras for an oplax monoidal monad, we always have a natural monoidal structures. The key observation is that the 2-category of lax monoidal monads in any 2-category D with finite products is isomorphic to the 2-category of monoidal objects with oplax morphisms in the 2-category of monads with lax morphisms in D. We explain at the end of the paper that a similar phenomenon occurs in many other situations.