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On the sphere spectrum from the viewpoint of linear logic
Abstract
In this note, we show the category of Γ-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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BibTeX
@misc{horiuchi2026sphere,
title = {{On the sphere spectrum from the viewpoint of linear logic}},
author = {Ryo Horiuchi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.13012},
eprint = {2608.13012},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13012},
}
RIS
TY - UNPB
TI - On the sphere spectrum from the viewpoint of linear logic
AU - Ryo Horiuchi
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2608.13012
UR - https://arxiv.org/abs/2608.13012
AB - In this note, we show the category of Γ-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.
ER -