Covers and Envelopes in Grothendieck Categories: Flat Covers of Complexes with Applications

By S.Tempest Aldrich, Edgar E. Enochs, J. R. G. Rozas, Luis Oyonarte. 2001

74 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/847cf8f02810cecc05913a2e0189ea85b4256ffe

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In Geometry and Topology

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Citations in the corpus

Gorenstein Projective, Injective, and Flat Complexes (2011, background): “such that: (1) Pi is a projective complex for all i ∈ ; (2) Ker 0 = G; (3) Hom P is exact for any projective complex P.”
Envelopes and Covers by Modules of Finite FP-Injective and Flat Dimensions (2007, unknown): “So the problem has been studied by many authors (see, for example, Aldrich et al., 2001a,b; Angeleri Hügel et al., 2006; Asensio Mayor and Martinez Hernandez, 1988; Bican et al., 2001; Chen and Ding, 1996; Ding, 1996; Eklof and Trlifaj, 2001; Enochs, 1981, 1984; Enochs and Jenda, 2000; Enochs and…”
Flat Covers in the Category of Quasi-coherent Sheaves Over the Projective Line (2004, background): “Some results guaranteeing the existence of general ℱ-covers and ℱ ⊥ -envelopes in Grothendieck categories with a projective generator have been proved provided that the class ℱ satisfies certain “standard” conditions (see, for example, Aldrich et al, 2001 , Corollaries 2.”
Deconstructibility and the Hill Lemma in Grothendieck categories (2010, methodology): “Kaplansky classes have been explicitly or implicitly used for proving approximation properties of flat modules or sheaves in various settings [2, 7, 9, 10, 11, 12], a fact which Gillespie [18] and Hovey [23] later applied in a crucial way to constructing monoidal model structures for complexes of sh”
Covers in finitely accessible categories (2010, methodology): “We point out the work of Aldrich, Enochs, Garćıa Rozas and Oyonarte [2] and El Bashir [14] in arbitrary Grothendieck categories, Enochs, Estrada, Garćıa Rozas and Oyonarte for quasi-coherent sheaves over the projective line [16] and for quasi-coherent sheaves over a scheme [17], Enochs and Oyonarte ”
Flat Covers and Flat Representations of Quivers (2004, unknown): “Proposition 4.1 (Aldrich et al., 2001, Corollary 2.12).”