Localization theory in higher homological algebra

We study localization theory in higher homological algebra, concentrating at the localizations of n-abelian and n-angulated categories. In both cases, starting with a class of morphisms S satisfying some natural conditions in an n-abelian category M, resp. n-angulated category C, we construct the localization of M, resp. C, at S which is an n-abelian, resp. n-angulated, category satisfying the relevant universal property. As a consequence, we construct new cluster tilting subcategories which arise as localizations of old ones. (c) 2023 Elsevier Inc. All rights reserved.