The Krull-Remak-Schmidt-Azumaya Theorem for Idempotent Complete Categories

Applied Categorical Structures 2026 Open access

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Authors: Simion Breaz
DOI: 10.1007/s10485-026-09888-6
Cited by: 0
References: 19

Abstract

Abstract We prove a version of the Krull-Remak-Schmidt-Azumaya unique decomposition theorem in idempotent complete additive categories. In particular, this result applies to compactly generated triangulated categories. In addition, we provide an example of an object with the finite exchange property that does not have the exchange property.

Fields of Study & Subjects

Rings Modules and Algebras Homotopy and Cohomology in Algebraic Topology Algebraic structures and combinatorial models

Publication details

Journal / source
Applied Categorical Structures
Publisher
Springer Science and Business Media LLC
Volume
34
Issue
5
Publication date
30 July 2026
Language
EN