查看文章

Higher homological algebra was introduced by Iyama. It is also known as -homological algebra where is a fixed integer, and it deals with -cluster tilting subcategories of abelian categories. All short exact sequences in such a subcategory are split, but it has nice exact sequences with objects. This was recently formalized by Jasso in the theory of -abelian categories. There is also a derived version of -homological algebra, formalized by Geiss, Keller, and Oppermann in the theory of -angulated categories (the reason for the shift from to is that angulated categories have triangulated categories as the “base case”). We introduce torsion classes and t-structures into the theory of -abelian and -angulated categories, and prove several results to motivate the definitions. Most of the results concern the -abelian and -angulated categories and associated to an -representation finite algebra  …