Higher Dimensional Ideal Approximation Theory

Ideal approximation theory is a gentle generalization of the clas- sical approximation theory and deals with morphisms and ideals instead of objects and subcategories. Our aim in this presentation is to study ideal ap- proximation theory over n-exact categories. In particular, the higher version of the notions such as ideal cotorsion pairs, phantom ideals, Salce s Lemma and Wakamatsu s Lemma for ideals will be introduced and studied. The main source of n-exact categories are n-cluster tilting subcategories of exact categories.