Right triangulated categories: As extriangulated categories, aisles and co-aisles

Abstract

Right triangulated categories can be thought of as triangulated categories whose shift functor is not an equivalence. We give intrinsic characterisations of when such categories have a natural extriangulated structure and are appearing as the (co-)aisle of a (co-)t-structure in an associated triangulated category.

28 pages, comments welcome!

References in corpus (3)

• On exact categories and applications to triangulated adjoints and model structures
• Positive and negative extensions in extriangulated categories
• Intervals of $s$-torsion pairs in extriangulated categories with negative first extensions

Cited by in corpus (1)

• From right (n+2)-angulated categories to n-exangulated categories