Monoidal category

English

Noun

1. Template:Lb A category $𝒞$ with a bifunctor $\otimes :𝒞\times 𝒞\to 𝒞$ which may be called tensor product, an associativity isomorphism ${\alpha }_{A,B,C}:(A\otimes B)\otimes C\simeq A\otimes (B\otimes C)$, an object $I$ which may be called tensor unit, a left unit natural isomorphism ${\lambda }_A:I\otimes A\simeq A$, a right unit natural isomorphism ${\rho }_A:A\otimes I\simeq A$, and some "coherence conditions" (pentagon and triangle commutative diagrams for those isomorphisms).