\(\otimes\)-strict AU categories (Q792442)

The author proves that a nonsymmetric monoidal category \({\mathcal A}\) is, as such, equivalent to a strict monoidal category \({\mathcal B}\). If \({\mathcal A}\) is symmetric, so is \({\mathcal B}\) and the equivalence respects the commutative law which, however, is not necessarily strict in \({\mathcal B}\). Corresponding results are obtained for categories with tensor products which do not have a distinguished ground object. The coherence theorems which do not involve symmetry morphisms are derived from these results.