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Deconstructibility and the Hill Lemma in Grothendieck categories
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January 3, 2013
Abstract.
A full subcategory of a Grothendieck category is called deconstructible if it consists of all transfinite extensions of some set of objects. This concept provides a handy framework for structure theory and construction of approximations for subcategories of Grothendieck categories. It also allows to construct model structures and t-structures on categories of complexes over a Grothendieck category. In this paper we aim to establish fundamental results on deconstructible classes and outline how to apply these in the areas mentioned above. This is related to recent work of Gillespie, Enochs, Estrada, Guil Asensio, Murfet, Neeman, Prest, Trlifaj and others.
Received: 2010-06-22
Published Online: 2013-01-03
Published in Print: 2013-01-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Grothendieck categories;
deconstructible classes;
Generalized Hill Lemma;
chain complexes
Articles in the same Issue
- Masthead
- Isomorphism criteria for Witt rings of real fields
- Simplicial differential calculus, divided differences, and construction of Weil functors
- Rank 3 permutation characters and maximal subgroups
- On the oscillation and nonoscillation of the solutions of impulsive differential equations of second order with retarded argument
- A note on the existence of transition probability densities of Lévy processes
- Carleson measures and Logvinenko–Sereda sets on compact manifolds
- Cofiniteness of composed local cohomology modules
- Real hypersurfaces of type (A) in complex two-plane Grassmannians related to the commuting shape operator
- Deconstructibility and the Hill Lemma in Grothendieck categories
