Quantum Quasigroups and the Quantum Yang-Baxter Equation

The self-dual concept of a quantum quasigroup offers a far-reaching unification of Hopf algebras (along with their non-associative extensions, e.g., [1–4]) and quasigroups [5]. Consider a bimagma (A,∇, ∆), an object of a strict symmetric monoidal category V with V-morphisms giving a magma structure or multiplication ∇ : A⊗ A→ A, and a comagma structure or comultiplication ∆ : A→ A⊗ A, such that ∆ is a magma homomorphism. (The latter bimagma condition is equivalent to its dual: ∇ is a comagma homomorphism.) A bimagma (A,∇, ∆) is a quantum quasigroup if two dual morphisms are invertible in V: the left composite