Deconstructibility and the Hill lemma in Grothendieck categories

Details Deconstructibility and the Hill lemma in Grothendieck categories Deconstructibility and the Hill lemma in Grothendieck categories

2010-05-18

arxiv.org/abs/1005.3251v2

Mathematics

Category Theory

20 pages; version 2: minor changes, misprints corrected, references updated

Scientific paper

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.

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