Ideal approximation theory in extriangulated categories

Abstract

In the present article, ideal approximation theory is introduced in extriangulated categories. To this end, Salce's Lemma, Christensen's Lemma, and Wakamatsu's Lemma are introduced and proved in an extriangulated category. It is also shown that a finite intersection of special precovering (respectively, special preenveloping) ideals remains special precovering (respectively, special preenveloping). The results in this article show that extriangulated categories are the appropriate context for developing ideal approximation theory.