Deconstructibility and the Hill Lemma in Grothendieck categories

By J. Št’ovíček. 2010

72 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/78c84debf13cfed7375148c1d0a2634410304bd7

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On exact categories and applications to triangulated adjoints and model structures (2010, background): “8] (see also [58]), we infer that F is deconstructible in Qco(X).”
Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves (2013, methodology): “Here we take a slightly restricted version of the result from [67], where also references to other versions and evolution stages of the Hill Lemma can be found.”
Models for singularity categories (2012, background): “2(2)] that Acyc(Z) ⊂ ChΓ (Z) is deconstructible (in [23] the result is proved for Γ = Z, but the arguments carry over to the case of a general grading group).”