Post-groups, post-groupoids and the Yang-Baxter equation

We introduce the notion of post-groups, which are the underlying structures of Rota-Baxter operators on groups. The differentiation of post-Lie groups gives post-Lie algebras. Post-groups are also related to braces and Lie-Butcher groups, and give rise to set-theoretical solutions of Yang-Baxter equations. We further introduce the notion of post-groupoids, whose differentiations are post-Lie algebroids. We show that post-groupoids give quiver-theoretical solutions of the Yang-Baxter equation on the underlying quiver of the subadjacent groupoids.
The talk is based on the joint work with Chengming Bai, Li Guo, Rong Tang and Chenchang Zhu.