What question did this study set out to answer?

To demonstrate that A infinity nerves of quasi-equivalent A infinity categories are weak-equivalent in the Joyal model structure.

March 4, 2026Open Access

Some Properties of the A -Nerve

Key Points

To demonstrate that A infinity nerves of quasi-equivalent A infinity categories are weak-equivalent in the Joyal model structure.
Proof of properties of A infinity nerves
Analysis of quasi-equivalence in A infinity categories
Application of the Joyal model structure
A infinity nerves of quasi-equivalent categories are shown to be weak-equivalent
The nerve of a pretriangulated A infinity category is established as a stable infinity-category

Abstract

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

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