Enriched Herds And Finite Quantum Groupoids

We describe a finite quantum groupoid associated to any finite Vect_k enriched herd.

💡 Research Summary

The paper introduces a categorical construction that associates a finite quantum groupoid—a weak Hopf algebra—to any finite Vectₖ‑enriched herd. After a brief motivation linking quantum groupoids, weak Hopf algebras, and categorical algebra, the authors recall the notion of a herd: a set of objects equipped with a binary operation that is associative only up to specified coherence, generalising groups and groupoids. Enrichment over Vectₖ replaces each hom‑set H(x, y) by a finite‑dimensional k‑vector space, thereby allowing linear combinations of morphisms and making the herd amenable to algebraic manipulation.

The central technical step is the formation of a coend \