The Karoubi envelope and weak idempotent completion of an extriangulated category

TL;DR

This paper demonstrates that the processes of idempotent and weak idempotent completion preserve the extriangulated structure of a category, expanding the understanding of their stability.

Contribution

It establishes that both idempotent and weak idempotent completions of an extriangulated category remain extriangulated, a result previously unknown.

Findings

Idempotent completion of an extriangulated category is extriangulated.

Weak idempotent completion of an extriangulated category is extriangulated.

The results extend the stability properties of extriangulated categories.

Abstract

We show that the idempotent completion and weak idempotent completion of an extriangulated category are also extriangulated.