## Model category structures on chain complexes of sheaves

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- by Mark Hovey PDF
- Trans. Amer. Math. Soc.
**353**(2001), 2441-2457 Request permission

## Abstract:

The unbounded derived category of a Grothendieck abelian category is the homotopy category of a Quillen model structure on the category of unbounded chain complexes, where the cofibrations are the injections. This folk theorem is apparently due to Joyal, and has been generalized recently by Beke. However, in most cases of interest, such as the category of sheaves on a ringed space or the category of quasi-coherent sheaves on a nice enough scheme, the abelian category in question also has a tensor product. The injective model structure is not well-suited to the tensor product. In this paper, we consider another method for constructing a model structure. We apply it to the category of sheaves on a well-behaved ringed space. The resulting flat model structure is compatible with the tensor product and all homomorphisms of ringed spaces.## References

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## Additional Information

**Mark Hovey**- Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
- Email: hovey@member.ams.org
- Received by editor(s): February 24, 2000
- Published electronically: January 3, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**353**(2001), 2441-2457 - MSC (2000): Primary 18F20, 14F05, 18E15, 18E30, 18G35, 55U35
- DOI: https://doi.org/10.1090/S0002-9947-01-02721-0
- MathSciNet review: 1814077