Heart of Irreducible Morphisms of Bounded Complexes

Abstract

In [9] Giraldo and Merklen studied irreducible morphisms in the categories 𝒞(𝒜) and D⁻(Λ), where 𝒞(𝒜) is the category of complexes over an abelian Krull–Schmidt category 𝒜 and D⁻(Λ) is the derived category of the bounded above complexes of finite generate left modules, over an Artin algebra Λ. In this work, we continue the study of irreducible morphism having one finite irreducible truncation.

Key Words:

• Category of complexes
• Derived category
• Irreducible morphisms
• Representation theory of algebras

2010 Mathematics Subject Classification:

• 16G10
• 16G70

ACKNOWLEDGMENTS

We are deeply thankful to the reviewer(s) for remarks and suggestions, particularly for Example 3.5.

Notes

Communicated by J. Zhang.