Abstract
We introduce a notion of total acyclicity associated to a subcat-egory 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.
Original language | English |
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Pages (from-to) | 99-118 |
Number of pages | 20 |
Journal | Contemporary Mathematics |
Volume | 751 |
DOIs | |
State | Published - 2020 |
Keywords
- Cotorsion pair
- Gorenstein object
- Stable category
- Totally acyclic complex