The categorified Diassociative cooperad

TL;DR

This paper constructs a categorified version of the Diassociative cooperad using quiver representations, enriching the algebraic structure within triangulated categories.

Contribution

It introduces a novel categorification of the linear dual of the Diassociative operad through quiver representations and triangulated categories.

Findings

Defines an anticyclic cooperad in triangulated categories

Provides a categorification of the linear dual of the Diassociative operad

Establishes connections between quiver representations and operad structures

Abstract

Using representations of quivers of type A, we define an anticyclic cooperad in the category of triangulated categories, which is a categorification of the linear dual of the Diassociative operad.