Theorem Lack Model Structure [efr-003I]

There is a model structure on the category \mathsf {BiCat}_s of bicategories and strict functors, in which

1. The weak equivalences are precisely the biequivalences, i.e. those (strict) functors which are equivalences on each hom-category, and surjective up to equivalence on objects
2. The fibrations are those functors F: \mathcal {C} \to \mathcal {D} with the equivalence lifting property, namely those that are isofibrations on each hom-category, and where given an object x \in \mathcal {C} and an equivalence f: F(x) \xrightarrow {\sim } y, there is a lift of f to an equivalence \tilde {f}: x \xrightarrow {\sim } \tilde {y}. We will also refer to these as equifibrations.