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arXiv · 2608.25804

De Morgan's Laws in Tensor-Triangular Geometry

Mark Lyttle
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Abstract

There is an isomorphism between the frame of radical thick tensor ideals of an essentially small tt-category and the frame of open sets of the Hochster dual of its Balmer spectrum. This isomorphism allows us to compare topological properties of the latter with tt-geometric properties of the former. We use this to give an intrinsic definition of those tt-categories which satisfy a variant of the second De Morgan law, and furthermore give a construction for producing such tt-categories.

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Mark Lyttle. 2026-08-26. De Morgan's Laws in Tensor-Triangular Geometry. https://arxiv.org/abs/2608.25804

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