S-protomodularity of the category of cocommutative bialgebras

Sterck, Florence
(2022) Journal of Algebra and its Applications — (2022)

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We prove that the category of cocommutative bialgebras in any locally presentable symmetric monoidal category 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 effective S-equivalence relations centralize each other as soon as the normal subobjects associated with them commute in the sense of Huq.
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Sterck, F. (2022). S-protomodularity of the category of cocommutative bialgebras. Journal of Algebra and its Applications. Published. https://doi.org/10.1142/s0219498823502523 (Original work published 2022)