Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theory
LW Christensen, S Estrada… - … combinatorial methods in …, 2020 - books.google.com
LW Christensen, S Estrada, P Thompson
Categorical, homological and combinatorial methods in algebra, 2020•books.google.comWe introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius
category, whose induced stable category is equivalent to the homotopy category of totally
acyclic complexes. Applied to the flat–cotorsion theory over a coherent ring, this provides a
new description of the category of cotorsion Gorenstein flat modules; one that puts it on
equal footing with the category of Gorenstein projective modules.
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius
category, whose induced stable category is equivalent to the homotopy category of totally
acyclic complexes. Applied to the flat–cotorsion theory over a coherent ring, this provides a
new description of the category of cotorsion Gorenstein flat modules; one that puts it on
equal footing with the category of Gorenstein projective modules.
Abstract
We introduce a notion of total acyclicity associated to a subcategory of an abelian category and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius category, whose induced stable category is equivalent to the homotopy category of totally acyclic complexes. Applied to the flat–cotorsion theory over a coherent ring, this provides a new description of the category of cotorsion Gorenstein flat modules; one that puts it on equal footing with the category of Gorenstein projective modules.
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