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We extend results of Br\"ustle-Yang on ideal quotients of 2-termsubcategories of perfect derived categories of non-positive dg algebras to arelative setting. We find a new interpretation of such quotients: they appearas prototypical examples of a new construction of quotients of extriangulatedcategories by ideals generated by morphisms from injectives to projectives. Weapply our results to Frobenius exact cluster categories and Higgs categorieswith suitable relative extriangulated structures, and to categories of walksrelated to gentle algebras. In all three cases, the extriangulated structuresare well-behaved (they are 0-Auslander) and their quotients are equivalent tohomotopy categories of two-term complexes of projectives over suitablefinite-dimensional algebras.

Extriangulated ideal quotients, with applications to cluster theory and gentle algebras