Abstract.
We make a general study of Quillen model structures on abelian categories. We show that they are closely related to cotorsion pairs, which were introduced by Salce [Sal79] and have been much studied recently by Enochs and coauthors [EJ00]. This gives a method of constructing model structures on abelian categories, which we illustrate by building two model structures on the category of modules over a (possibly noncommutative) Gorenstein ring. The homotopy category of these model structures is a generalization of the stable module category much used in modular representation theory. This stable module category has also been studied by Benson [Ben97].
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 14 December 2000; in final form: 17 December 2001 / Published online: 5 September 2002
Rights and permissions
About this article
Cite this article
Hovey, M. Cotorsion pairs, model category structures, and representation theory. Math Z 241, 553–592 (2002). https://doi.org/10.1007/s00209-002-0431-9
Issue Date:
DOI: https://doi.org/10.1007/s00209-002-0431-9