Opmonoidal monads

Paddy McCrudden

Hopf monads are identified with monads in the 2-category Opmon of monoidal categories, opmonoidal functors and transformations. Using Eilenberg-Moore objects, it is shown that for a Hopf monad $S$, the categories Alg(Coalg($S$)) and Coalg(Alg($S$)) are canonically isomorphic. The monadic arrows Opmon are then characterized. Finally, the theory of multicategories and a generalization of structure and semantics are used to identify the categories of algebras of Hopf monads.

Keywords: Hopf Monad, Eilenberg Moore Algebras, Multicategories, Structure and Semantics.

2000 MSC: 18D10, 18D25, 18D05.

Theory and Applications of Categories, Vol. 10, 2002, No. 19, pp 469-485.


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