Exact triangles as modules over an $A_\infty$-category

TL;DR

This paper constructs a strictly-unital $A_ fty$-category where representations correspond to exact triangles, making the three-fold symmetry of these triangles explicit within the category's structure.

Contribution

It introduces an $A_ abla$-category with representations as exact triangles, highlighting the three-fold symmetry directly in the $A_ abla$-category framework.

Findings

Explicit $A_ abla$-category modeling exact triangles

Manifestation of three-fold symmetry in the $A_ abla$-category

Representation theory of exact triangles within $A_ abla$-categories

Abstract

This note describes a strictly-unital $A_\infty$-category whose representations are exact triangles such that the three-fold symmetry on exact triangles is manifest on the $A_\infty$-category.