Some Properties of the $$\text{ A}_{\infty }$$-Nerve
Abstract
Abstract The aim of this paper is to prove that the $$\text{ A}_{\infty }$$ A ∞ -nerve of two quasi-equivalent $$\text{ A}_{\infty }$$ A ∞ -categories (linear over a commutative ring) are weak-equivalent in the Joyal model structure. As a consequence we prove that the $$\text{ A}_{\infty }$$ A ∞ -nerve of a pretriangulated $$\text{ A}_{\infty }$$ A ∞ -category is a stable $$\infty $$ ∞ -category.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Publication details
- Journal / source
- Milan Journal of Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 94
- Issue
- 1
- Pages
- 45–70
- Publication date
- 2 March 2026
- Language
- EN