The flat model structure on

Author:
James Gillespie

Translated by:

Journal:
Trans. Amer. Math. Soc. **356** (2004), 3369-3390

MSC (2000):
Primary 55U35, 18G35, 18G15

Published electronically:
January 29, 2004

MathSciNet review:
2052954

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Abstract: Given a cotorsion pair in an abelian category with enough objects and enough objects, we define two cotorsion pairs in the category of unbounded chain complexes. We see that these two cotorsion pairs are related in a nice way when is hereditary. We then show that both of these induced cotorsion pairs are complete when is the ``flat'' cotorsion pair of -modules. This proves the flat cover conjecture for (possibly unbounded) chain complexes and also gives us a new ``flat'' model category structure on . In the last section we use the theory of model categories to show that we can define using a flat resolution of and a cotorsion coresolution of .

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Additional Information

**James Gillespie**

Affiliation:
Department of Mathematics, 4000 University Drive, Penn State–McKeesport, McKeesport, Pennsylvania 15132-7698

Email:
jrg21@psu.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-04-03416-6

Received by editor(s):
October 1, 2002

Received by editor(s) in revised form:
May 13, 2003

Published electronically:
January 29, 2004

Additional Notes:
The author thanks Mark Hovey of Wesleyan University

Article copyright:
© Copyright 2004
American Mathematical Society