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<p>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.</p>

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

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  • 出版模式：

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  • 发表日期：

    2026年7月30日

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  • Simion Breaz

摘要

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.