Geodesic
Opmonoidal monads
Theory and applications of categories, Tome 10 (2002), pp. 469-485

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 18D10, 18D25, 18D05.
Keywords: Hopf Monad, Eilenberg Moore Algebras, Multicategories, Structure and Semantics. 
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     author = {Paddy McCrudden},
     title = {Opmonoidal monads},
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     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2002_10_a18/}
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Paddy McCrudden. Opmonoidal monads. Theory and applications of categories, Tome 10 (2002), pp. 469-485. http://geodesic.mathdoc.fr/item/TAC_2002_10_a18/