Hearts of twin cotorsion pairs on extriangulated categories

By Yu Liu, Hiroyuki Nakaoka. Journal of Algebra, 2017

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In this article, we study the heart of a cotorsion pairs on an exact category and a triangulated category in a unified meathod, by means of the notion of an extriangulated category. We prove that the heart is abelian, and construct a cohomological functor to the heart. If the extriangulated category has enough projectives, this functor gives an equivalence between the heart and the category of coherent functors over the coheart modulo projectives. We also show how an n-cluster tilting subcategory of an extriangulated category gives rise to a family of cotorsion pairs with equivalent hearts.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2fb333cb347b6b39fcb195d0b1ae96b7ceed00e9

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors (2019, methodology): “They appear in representation theory in relationwith cotorsion pairs [29, 58, 59, 104], with Auslander–Reiten theory [51], with cluster algebras, mutations, or cluster-tilting theory [29, 63–65, 83, 106], with Cohen–Macaulay dg-modules in the remarkable [53].”