From the 3 of 6 linked papers with an AI index.
6 papers
is not algebraically coherent
Andrea Sciandra, Vito Volpe
The authors prove that the category SKB is not algebraically coherent, which consequently means it is not locally algebraically cartesian closed, and they extend this result to coc…
An infinitesimal deformation of the post-Lie and post-Hopf algebra correspondence
Andrea Rivezzi, Andrea Sciandra, Thomas Weber
The paper studies infinitesimal deformations of post‑Lie and post‑Hopf algebras, showing compatibility with the universal enveloping algebra and primitive element functors, and est…
Protomodularity of cocommutative Hopf monoids in duoidal categories and quasitriangular Hopf algebras
Alessandro Ardizzoni, Lucrezia Bottegoni, Alan Cigoli +1
The paper generalizes the protomodular structure of cocommutative Hopf algebras to quasitriangular Hopf algebras by treating them as cocommutative bimonoids in tensor‑braided duoid…
Central series of cocommutative Hopf braces
Maria Bevilacqua, Marino Gran, Andrea Sciandra
By extending some classical results known for groups and skew braces, we define and investigate central series of cocommutative Hopf braces. Both left and right central series are…
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…