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math.GR2025
Split Lemma and First Isomorphism Theorem for groupoids
Davide Ferri
Groupoids are the oidification of groups, and they are largely used in topology and representation theory. We consider here the category of all groupoids with all mo…
math.QA2025
Reflections and Drinfeld twists for set-theoretic Yang-Baxter maps
Davide Ferri
The Yang-Baxter equation (YBE) and the reflection equation (RE) both come from mathematical physics, and they can be defined in any monoidal category. For cartesian monoidal catego…
math.QA2025
Structure groupoids of quiver-theoretic Yang-Baxter maps
Davide Ferri, Youichi Shibukawa
Solutions to the quiver-theoretic quantum Yang-Baxter equation are associated with structure categories and structure groupoids. We prove that the structure groupoids of involutive…