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Complete cotorsion pairs in exact categories. (English) Zbl 1469.18012

Summary: We generalize a theorem of M. Saorín and J. Šťovíček [Adv. Math. 228, No. 2, 968–1007 (2011; Zbl 1235.18010)] on complete cotorsion pairs in exact categories. Our proof is based on a generalized small object argument due to [B. Chorny, J. Pure Appl. Algebra 204, No. 3, 568–583 (2006; Zbl 1086.55012)]. As a consequence, we cover some examples which are not covered by the result of Saorín-Štovíček [loc. cit.].

MSC:

18E10 Abelian categories, Grothendieck categories
18G25 Relative homological algebra, projective classes (category-theoretic aspects)
18G35 Chain complexes (category-theoretic aspects), dg categories
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References:

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