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math.RA2026
Braidings, duoidal categories and pre-Cartier structures for bi(co)modules
Andrea Sciandra, Lukas Simons
We study braidings and infinitesimal braidings on categories of bi(co)modules and tetramodules, and their compatibility with duoidal structures. For an arbitrary coalgebra, we clas…
math.RA2026
Associativity of the -product of skew braces
Andrea Sciandra
For braces, associativity of the -product is equivalent to two-sidedness. We extend this result to skew braces by proving that any two of the following conditions imply the…
math.RA2026
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…