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Higher homological algebra was introduced by Iyama. It is also known as n-homological algebra where n 2 is a fixed integer, and it deals with n-cluster tilting subcategories of abelian categories. All short exact sequences in such a subcategory are split, but it has nice exact sequences with n + 2 objects. This was recently formalised by Jasso in the theory of n-abelian categories. There is also a derived version of n-homological algebra, formalised by Geiss, Keller, and Oppermann in the theorydoi:10.1093/imrn/rnv265 fatcat:ayvlzun3mnbtnpgs7i2a2zcdja