Abstract
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 in. 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 k2Ã2.
Original language | English |
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Pages (from-to) | 4567-4583 |
Number of pages | 17 |
Journal | Communications in Algebra |
Volume | 39 |
Issue number | 12 |
DOIs | |
Publication status | Published - 2011 |
Keywords
- Eilenberg, Moore spectral sequences
- arrow categories
- monads
- triples_theory of
- weak distributive laws
- weak lifting