On the 2-categories of weak distributive laws | Macquarie University ResearchOnline

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Title: On the 2-categories of weak distributive laws
Related: Communications in algebra, Vol. 39, Issue 12, (2011), p.4567-4583
DOI: 10.1080/00927872.2011.616436
Publisher: Taylor & Francis
Date: 2011
Author/Creator: Böhm, Gabriella
Author/Creator: Lack, Stephen
Author/Creator: Street, Ross
Description: A weak mixed distributive law (also called weak entwining structure [8]) in a 2-category consists of a monad and a comonad, together with a 2-cell relating them in a way which generalizes a mixed distributive law due to Beck. We show that a weak mixed distributive law can be described as a compatible pair of a monad and a comonad, in 2-categories extending, respectively, the 2-category of comonads and the 2-category of monads in [13]. Based on this observation, we define a 2-category whose 0-cells are weak mixed distributive laws. In a 2-category K which admits Eilenberg–Moore constructions both for monads and comonads, and in which idempotent 2-cells split, we construct a fully faithful 2-functor from this 2-category of weak mixed distributive laws to K2×2.
Description: 17 page(s)
Subject Keyword: Arrow 2-category
Subject Keyword: Eilenberg–Moore object
Subject Keyword: Monad
Subject Keyword: Weak distributive law
Subject Keyword: Weak lifting
Resource Type: journal article
Organisation: Macquarie University. Dept. of Mathematics

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