Equivalence of hearts of twin cotorsion pairs on triangulated categories
Hiroyuki Nakaoka
TL;DR
This paper explores conditions under which the hearts of twin cotorsion pairs in triangulated categories are equivalent, focusing on the vanishing of certain components related to associated functors.
Contribution
It establishes criteria for the equivalence of hearts of twin cotorsion pairs, linking it to the vanishing of specific components via associated functors.
Findings
Identifies conditions for heart equivalence in twin cotorsion pairs
Connects heart equivalence to vanishing components in associated functors
Provides a framework for understanding cotorsion pair relationships
Abstract
In this article, we investigate the condition for the hearts of twin cotorsion pairs to be equivalent, compatibly with the associated functors. This is related to the vanishing of components of pairs through the associated functors.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology