Some properties of the A${}_{\infty }$-nerve

Abstract

The aim of this paper is to prove that the A${}_{\infty }$-nerve of two quasi-equivalent A${}_{\infty }$-categories (linear over a commutative ring) are weak-equivalent in the Joyal model structure. As a consequence we prove that the A${}_{\infty }$-nerve of a pretriangulated A${}_{\infty }$-category is a stable $\infty$-category.

21 pages. Updated version. We extended the previous results to categories linear over a commutative ring. Comments are welcome