Geodesic
Pivotal objects in monoidal categories and their Hopf monads
Theory and applications of categories, Tome 37 (2021), pp. 287-325

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

A pair of objects (P,Q) in a monoidal category C, is called a pivotal pair if there exist a family of duality morphisms, making Q both a left dual and a right dual of P. We introduce the correct notion of morphisms between such pairs, and thereby define the pivotal cover of a monoidal category. Given such a pair (P,Q), we construct the category C(P,Q), of objects which intertwine with P and Q in a compatible manner and show that C(P,Q) lifts the monoidal structure of C as well as the closed structure of C, when C is closed. If C has suitable colimits, we construct a family of Hopf monads which correspond to such pairs in C and present the resulting families of braided Hopf algebras and Hopf algebroids, when C is a braided category or the category of bimodules over a base algebra, respectively.

Publié le :
Classification : 18M05, 18D15, 16T99, 18C20
Keywords: Monoidal category, closed category, pivotal category, Hopf monad, Hopf algebra, tensor category 
@article{TAC_2021_37_a10,
     author = {Aryan Ghobadi},
     title = {Pivotal objects in monoidal categories  and their {Hopf} monads},
     journal = {Theory and applications of categories},
     pages = {287--325},
     publisher = {mathdoc},
     volume = {37},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_37_a10/}
}
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Aryan Ghobadi. Pivotal objects in monoidal categories  and their Hopf monads. Theory and applications of categories, Tome 37 (2021), pp. 287-325. http://geodesic.mathdoc.fr/item/TAC_2021_37_a10/