On exact categories and applications to triangulated adjoints and model structures
By Manuel Saor'in, J. Št’ovíček. 2010
114 citations recorded by the source corpus.
Abstract We show that Quillenʼs small object argument works for exact categories under very mild conditions. This has immediate applications to cotorsion pairs and their relation to the existence of certain triangulated adjoint functors and model structures. In particular, the interplay of different exact structures on the category of complexes of quasi-coherent sheaves leads to a streamlined and generalized version of recent results obtained by Estrada, Gillespie, Guil Asensio, Hovey, Jorgensen, Neeman, Murfet, Prest, Trlifaj and possibly others.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ef5b2a4813f4940e70321a66bd552c93dcac2df8
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In Geometry and Topology
- J. Št’ovíček
- Blas Torrecillas
- P. Asensio
- Ivo Herzog
- X. Fu
- Lidia Angeleri Hugel
- L. Positselski
- Manuel Saor'in
In Mathematical Physics
- J. Št’ovíček
- Blas Torrecillas
- P. Asensio
- Ivo Herzog
- X. Fu
- Lidia Angeleri Hugel
- L. Positselski
- Manuel Saor'in
In Statistical and Nonlinear Physics
Citations in the corpus
- Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves (2013, methodology): “A recipe for their construction has been found by Gillespie [27, 28, 29] and various versions of the result were discussed in [23, 65], but our presentation here is based on an elegant idea from [71].”
- Deconstructibility and the Hill Lemma in Grothendieck categories (2010, methodology): “I would like to thank Manuel Saoŕın, my co-author in [30], for useful discussions and especially for suggesting Proposition 4.”
- Ideal approximation theory (2013, methodology): “Expositions of approximation theory for categories of modules may be found in the monographs of Beligiannis and Reiten [4] and Göbel and Trlifaj [17], but cotorsion pairs have also been used to study approximation theory in sheaf categories [13], general Grothendieck categories [15,20], and more abs”