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

Abstract

Evidence is given for the correctness of the Joyal-Riehl-Verity construction of the homotopy bicategory of the $(\infty ,2)$-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.

31 pages, LaTeX. Fixed a typo; added a reference to the new Riehl-Verity preprint