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The Krull-Remak-Schmidt-Azumaya Theorem for idempotent complete categories

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arxiv 2503.21216 v2 pith:UHIOJWM6 submitted 2025-03-27 math.CT

Simion Breaz This is my paper · ORCID
classification math.CT
keywords categoriescompleteexchangeidempotentkrull-remak-schmidt-azumayapropertytheoremaddition
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We prove that the Krull-Remak-Schmidt-Azumaya unique decomposition theorem holds in idempotent complete additive categories with enough compact objects. 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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  1. Induction for extended affine type A Soergel bimodules: first steps

    math.RT 2025-07 accept novelty 6.0 of 10

    A categorical embedding Ψ for extended affine type A Soergel bimodules is constructed, categorifying the Hecke algebra parabolic embedding, with an example categorifying the Zelevinsky tensor product of two trivial re...

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