The homotopy bicategory of $(\mathrm{\infty },1)$-categories

Evidence is given for the correctness of the Joyal-Riehl-Verity construction of the homotopy bicategory of the $(\mathrm{\infty },2)$-category of $(\infty, 1)$-categories; in particular, it is shown that the analogous construction using complete Segal spaces instead of quasicategories yields a bicategorically equivalent 2-category.