Deconstructibility and the Hill lemma in Grothendieck categories
Category Theory
2013-01-14 v2 Algebraic Geometry
Representation Theory
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.
Keywords
Cite
@article{arxiv.1005.3251,
title = {Deconstructibility and the Hill lemma in Grothendieck categories},
author = {Jan Stovicek},
journal= {arXiv preprint arXiv:1005.3251},
year = {2013}
}
Comments
20 pages; version 2: minor changes, misprints corrected, references updated