Cotorsion Pairs and Cartan–Eilenberg Categories

Abstract

Cartan-Eilenberg categories were recently introduced by Guillén Santos, Navarro Aznar, Pascual and Roig. In the present paper, we give a method of constructing Cartan-Eilenberg categories for abelian categories, based on cotorsion pairs. In particular, we recover the left Cartan-Eilenberg structure for (un)bounded below chain complexes of modules (Pascual, Collect Math 63(2):203-216, 2012) and extend it to more general categories, including the category of (quasicoherent)sheaves over a projective scheme.Mathematics Subject Classification. 18E35, 18G25, 18G35, 18G55.