%0 Journal Article %1 lack2002formal %A Lack, Stephen %A Street, Ross %D 2002 %J Journal of Pure and Applied Algebra %K category monad %N 1–3 %P 243 - 265 %R http://dx.doi.org/10.1016/S0022-4049(02)00137-8 %T The formal theory of monads \II\ %U http://www.sciencedirect.com/science/article/pii/S0022404902001378 %V 175 %X We give an explicit description of the free completion EM(K) of a 2-category K under the Eilenberg–Moore construction, and show that this has the same underlying category as the 2-category Mnd(K) of monads in K. We then demonstrate that much of the formal theory of monads can be deduced using only the universal property of this completion, provided that one is willing to work with EM(K) as the 2-category of monads rather than Mnd(K). We also introduce the wreaths in K; these are the objects of EM(EM(K)), and are to be thought of as generalized distributive laws. We study these wreaths, and give examples to show how they arise in a variety of contexts.

@article{lack2002formal, abstract = {We give an explicit description of the free completion EM(K) of a 2-category K under the Eilenberg–Moore construction, and show that this has the same underlying category as the 2-category Mnd(K) of monads in K. We then demonstrate that much of the formal theory of monads can be deduced using only the universal property of this completion, provided that one is willing to work with EM(K) as the 2-category of monads rather than Mnd(K). We also introduce the wreaths in K; these are the objects of EM(EM(K)), and are to be thought of as generalized distributive laws. We study these wreaths, and give examples to show how they arise in a variety of contexts. }, added-at = {2015-01-11T04:34:05.000+0100}, author = {Lack, Stephen and Street, Ross}, biburl = {https://www.bibsonomy.org/bibtex/2f109d5fc2e062d0b067a4824e41fcea9/t.uemura}, description = {The formal theory of monads II}, doi = {http://dx.doi.org/10.1016/S0022-4049(02)00137-8}, interhash = {d514461545be8ace3fe71be625009692}, intrahash = {f109d5fc2e062d0b067a4824e41fcea9}, issn = {0022-4049}, journal = {Journal of Pure and Applied Algebra }, keywords = {category monad}, note = {Special Volume celebrating the 70th birthday of Professor Max Kelly }, number = {1–3}, pages = {243 - 265}, timestamp = {2015-01-11T04:34:05.000+0100}, title = {The formal theory of monads \{II\} }, url = {http://www.sciencedirect.com/science/article/pii/S0022404902001378}, volume = 175, year = 2002 }