Abstract
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.
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