A comparison between pretriangulated A_∞-categories and ∞-Stable categories

2016/09/02 by Ornaghi, Mattia
#Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.00566

Abstract

In this paper we will prove that the A_∞-nerve of two quasi-equivalent A_∞-categories are weak-equivalent in the Joyal model structure, a consequence of this fact is that the A_∞-nerve of a pretriangulated A_∞-category is ∞-stable. Moreover we give a comparison between the notions of pretriangulated A_∞-categories, pretriangulated dg-categories and ∞-stable categories.

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