Model bicategories and their homotopy bicategories

We give the definitions of model bicategory and q-homotopy, which are natural generalizations notions category homotopy to context bicategories. For any C, denote by Cfc full sub-bicategory fibrant-cofibrant objects. prove that 2-dimensional localization C at weak equivalences can be computed as a Ho(C) whose objects arrows those 2-cells classes q-homotopies up an equivalence relation. When considered for category, coincide with homotopies Quillen. The pseudofunctor C⟶qHo(C) yields is constructed using notion replacement in this context. include appendix general result independent interest on transfer structure lax functors, we apply obtain replacement.