monoidal category

== English == === Noun === monoidal category (plural monoidal categories) (category theory) A category C {\displaystyle {\mathcal {C}}} with a bifunctor ⊗ : C × C → C {\displaystyle \otimes :{\mathcal {C}}\times {\mathcal {C}}\rightarrow {\mathcal {C}}} which may be called tensor product, an associativity isomorphism α A , B , C : ( A ⊗ B ) ⊗ C ≃ A ⊗ ( B ⊗ C ) {\displaystyle \alpha _{A,B,C}:(A\otimes B)\otimes C\simeq A\otimes (B\otimes C)} , an object I {\displaystyle I} which may be called tensor unit, a left unit natural isomorphism λ A : I ⊗ A ≃ A {\displaystyle \lambda _{A}:I\otimes A\simeq A} , a right unit natural isomorphism ρ A : A ⊗ I ≃ A {\displaystyle \rho _{A}:A\otimes I\simeq A} , and some "coherence conditions" (pentagon and triangle commutative diagrams for those isomorphisms).