Ideal balanced pairs in n-exangulated categories

Abstract

This paper is devoted to ideal approximation theory in $n$-exangulated categories. We define ideal balanced pairs and explore their properties and equivalent characterizations. We prove that any complete ideal cotorsion triple $(\mathcal{I},\mathcal{K},\mathcal{J})$ satisfying suitable assumptions yields an ideal balanced pair $(\mathcal{I}, \mathcal{J})$, and the converse holds under additional hypotheses. We further show that for an ideal balanced pair, it is equivalent to an additive subfunctor with enough projective morphisms and enough injective morphisms.