In higher Auslander algebras of type A, the d-almost positive subcategory is the d-exangulated quotient of the d-exact subcategory of the module category and the (d+2)-angulated cluster category by ideals from injective-to-projective morphisms.
Exact dg categories I: foundations
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n-exact dg-categories are introduced so that their homotopy categories carry n-exangulated structures when Hom-cohomologies vanish, and n-cluster tilting subcategories of exact dg-categories naturally become n-exact dg-categories.
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Relations between categorifications of higher-dimensional type $A$ cluster combinatorics
In higher Auslander algebras of type A, the d-almost positive subcategory is the d-exangulated quotient of the d-exact subcategory of the module category and the (d+2)-angulated cluster category by ideals from injective-to-projective morphisms.