- Date
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Thursday 19 December 2024, 9.30 - 10.30
- Abstract
- The Yang–Baxter equation (YBE) can be defined in any monoidal category. It is already well known and studied in at least two categories, namely vector spaces (Veck) and sets (Set). Quivers over a given set of vertices are also a monoidal category: here, the YBE is less understood, but still relevant. We describe notions of braided groupoids (Andruskiewitsch, 2005) and skew bracoids in the sense of Sheng–Tang–Zhu (2024). We relate them to the notion of dynamical skew brace (Matsumoto, 2013), and we describe the rich combinatorics of these structures (DF, 2024), depending on some strings of integer invariants. The theory of racks and quandles does not translate well in the quiver-theoretic setting. We briefly discuss what works and what does not; and how “rack-like” solutions can be constructed in this framework.
