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is not algebraically coherent
Andrea Sciandra, Vito Volpe
We prove that the category is not algebraically coherent. As a consequence, it is not locally algebraically cartesian closed. Then the same can be deduced for cocomm…
Protomodularity of cocommutative Hopf monoids in duoidal categories and quasitriangular Hopf algebras
Alessandro Ardizzoni, Lucrezia Bottegoni, Alan Cigoli +1
In this work, we extend the protomodularity of the category of cocommutative Hopf algebras to the quasitriangular setting. Every quasitriangular Hopf algebra admits a minimal quasi…
On the semi-abelianness of cocommutative Hopf monoids
Andrea Sciandra, Zhenbang Zuo
By providing a suitable generalization of Newman's bijective correspondence known for cocommutative Hopf algebras, we prove that the category of cocommutative Hopf monoids in any a…
Hopf formulae for cocommutative Hopf algebras
Marino Gran, Andrea Sciandra
The adjunction between coalgebras and Hopf algebras, first described by Takeuchi, allows one to prove that the semi-abelian category of cocommutative Hopf algebras has enough $\mat…