The aim of this paper is to prove that the A∞-nerve of two quasi-equivalent A∞-categories (linear over a commutative ring) are weak-equivalent in the Joyal model structure. As a consequence we prove that the A∞-nerve of a pretriangulated A∞-category is a stable ∞-category.
Some Properties of the $$\text{ A}_{\infty }$$-Nerve / M. Ornaghi. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - (2026), pp. 1-26. [Epub ahead of print] [10.1007/s00032-026-00429-3]
Some Properties of the $$\text{ A}_{\infty }$$-Nerve
M. Ornaghi
2026
Abstract
The aim of this paper is to prove that the A∞-nerve of two quasi-equivalent A∞-categories (linear over a commutative ring) are weak-equivalent in the Joyal model structure. As a consequence we prove that the A∞-nerve of a pretriangulated A∞-category is a stable ∞-category.
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