The Homotopy Theory of $A_{\infty }$Categories

Abstract

In this paper we describe the homotopy category of the $A_{\infty }$categories. To do that we introduce the notion of semi-free $A_{\infty }$category, which plays the role of standard cofibration. Moreover, we define the non unital $A_{\infty }$ (resp. DG)categories with cofibrant morphisms and we prove that any non unital $A_{\infty }$ (resp. DG)category has a resolution of this kind.

49 pages, 5 figures

References in corpus (1)

• The uniqueness problem of dg-lifts and Fourier-Mukai kernels