2022/01/17 by Florence Sterck, Florence, Sterck
Mathematics · #16T10 #18E13 #18M05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2201.06520
openalex publication_date 2022/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the category of cocommutative bialgebras in any symmetric monoidal category (that has equalizers) is an S-protomodular category with respect to a particular class of split extensions of cocommutative bialgebras. We also obtain the ``partial'' well-known Smith is Huq condition, meaning that two S-equivalence relations centralize each other as soon as the normal subobjects associated with them commute in the sense of Huq.