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The flat model structure on  |
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| Authors: | James Gillespie |
| Affiliation: | Department of Mathematics, 4000 University Drive, Penn State--McKeesport, McKeesport, Pennsylvania 15132-7698 |
| 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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