Mathematics – Category Theory
Scientific paper
2010-09-17
Comm. Algebra 39 (2011), no. 12, 4567-4583
Mathematics
Category Theory
15 pages LaTeX source, final version to appear in Comm. Algebra
Scientific paper
10.1080/00927872.2011.616436
A weak mixed distributive law (also called weak entwining structure) 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. 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 K^{2 x 2}.
Böhm Gabriella
Lack Stephen
Street Ross
No associations
LandOfFree
On the 2-categories of weak distributive laws does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the 2-categories of weak distributive laws, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the 2-categories of weak distributive laws will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-442480