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A Hopf algebra object in Loday and Pirashvili's category of linear mapsentails an ordinary Hopf algebra and a Yetter-Drinfel'd module. We equip thelatter with a structure of a braided Leibniz algebra. This provides a unifiedframework for examples of racks in the category of coalgebras discussedrecently by Carter, Crans, Elhamdadi and Saito.

Racks, Leibniz algebras and Yetter-Drinfel'd modules