Derived, coderived, and contraderived categories of locally presentable abelian categories

0545361 - MÚ 2023 RIV NL eng J - Článek v odborném periodiku
Positselski, Leonid - Šťovíček, J.
Derived, coderived, and contraderived categories of locally presentable abelian categories.
Journal of Pure and Applied Algebra. Roč. 226, č. 4 (2022), č. článku 106883. ISSN 0022-4049. E-ISSN 1873-1376
Grant CEP: GA ČR(CZ) GA20-13778S
Institucionální podpora: RVO:67985840
Klíčová slova: conventional and exotic derived categories * complete cotorsion pairs * abelian model structures
Obor OECD: Pure mathematics
Impakt faktor: 0.8, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jpaa.2021.106883

For a locally presentable abelian category B with a projective generator, we construct the projective derived and contraderived model structures on the category of complexes, proving in particular the existence of enough homotopy projective complexes of projective objects. We also show that the derived category D(B) is generated, as a triangulated category with coproducts, by the projective generator of B. For a Grothendieck abelian category A, we construct the injective derived and coderived model structures on complexes. Assuming Vopěnka’s principle, we prove that the derived category D(A) is generated, as a triangulated category with products, by the injective cogenerator of A. We also define the notion of an exact category with an object size function and prove that the derived category of any such exact category with exact κ-directed colimits of chains of admissible monomorphisms has Hom sets. Hence the derived category of any locally presentable abelian category has Hom sets.
Trvalý link: http://hdl.handle.net/11104/0322070