On the sphere spectrum from the viewpoint of linear logic

Ryo Horiuchi

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arXiv · 2608.13012

On the sphere spectrum from the viewpoint of linear logic

Ryo Horiuchi

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Abstract

In this note, we show the category of $\Gamma$-sets with the sphere spectrum, the smash product, and the substitution product gives rise to an isomix linearly distributive category, which is a categorical semantics of the multiplicative fragment of linear logic. We also show Lydakis' assembly map between these two monoidal products corresponds to the mixor.

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Ryo Horiuchi. 2026-08-13. On the sphere spectrum from the viewpoint of linear logic. https://arxiv.org/abs/2608.13012

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