nLab wreath



Higher algebra

2-Category theory



A wreath is a generalisation of a distributive law between two monads in a 2-category. While a distributive law in a 2-category KK can be seen as an object of Mnd(Mnd(K))Mnd(Mnd(K)), a wreath can be seen as an object of EM(EM(K))EM(EM(K)), where EMEM denotes the completion of a 2-category under Eilenberg–Moore objects. Since EMEM is a 2-monad, the multiplication EMEMEMEM \circ EM \to EM produces from every wreath a composite monad.


  • Steve Lack, Ross Street, The formal theory of monads II, Special volume celebrating the 70th birthday of Professor Max Kelly.

    J. Pure Appl. Algebra 175 (2002), no. 1-3, 243–265.

  • Dimitri Chikhladze, A note on warpings of monoidal structures, arXiv:1510.00483 (2015).

Last revised on April 29, 2024 at 21:22:50. See the history of this page for a list of all contributions to it.