Concrete categories are concretely equivalent iff their uniquely transportable modifications are strict concretely isomorphic (Q1364916)

In this paper, a concrete functor from a concrete category \(({\mathcal A}, U)\) to another one \(({\mathcal B}, V)\) is a functor \(F: {\mathcal A} \to {\mathcal B}\) together with a natural isomorphism \(\varphi: VF\to U\). It is strict if \(\varphi\) is the identity. It is a concrete equivalence if it has a concrete quasi-inverse, as usually. It is proved that using transport of structure, concrete equivalences give rise to strict ones.