Hereditary cotorsion pairs and silting subcategories in extriangulated categories
Takahide Adachi, Mayu Tsukamoto
TL;DR
This paper explores the structure of cotorsion pairs in extriangulated categories, establishing a connection with silting subcategories and analyzing the poset relationships within these mathematical frameworks.
Contribution
It introduces a bijection between bounded hereditary cotorsion pairs and silting subcategories in extriangulated categories, advancing the understanding of their interrelations.
Findings
Established a relationship between cotorsion pairs and their hearts.
Proved a bijection between hereditary cotorsion pairs and silting subcategories.
Analyzed the poset structure of cotorsion pairs.
Abstract
In this paper, we study (complete) cotorsion pairs in extriangulated categories. First, we study a relationship between an interval of the poset of cotorsion pairs and the poset of cotorsion pairs in the heart associated to the interval. Secondly, we establish a bijection between bounded hereditary cotorsion pairs and silting subcategories in extriangulated categories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology