This research proves a unique decomposition theorem in idempotent complete additive categories, highlighting its application.
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.
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Simion Breaz (2026) studied this question.
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