Relative tilting theory in extriangulated categories
Chenbei Xie
TL;DR
This paper extends approximation theory and tilting concepts to extriangulated categories by defining relative resolutions and coresolutions, providing a broader framework for understanding these structures.
Contribution
It introduces relative resolutions and coresolutions in extriangulated categories, generalizing Auslander-Buchweitz theory and developing relative tilting object theories.
Findings
Generalization of Auslander-Buchweitz approximation theory
Development of relative tilting object theories
Framework for relative resolutions in extriangulated categories
Abstract
In this article, we define relative resolutions and coresolutions in extriangulated categories. By studying this relative resolutions and coresolutions, we get a generalization of the Auslander-Buchweitz approximation theory. Finally, we develop some theories of relative tilting objects in extriangulated categories.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology