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math.CT2026
On the sphere spectrum from the viewpoint of linear logic
Ryo Horiuchi
In this note, we show the category of -sets with the sphere spectrum, the smash product, and the substitution product gives rise to an isomix linearly distributive category, whi…
math.CT2025
On the Witt vectors in the Lawvere quantale
Ryo Horiuchi
In this note, we investigate the Witt vectors in the min-plus algebra of extended non-negative real numbers, and consider categories enriched over them viewed as a monoidal categor…
math.CT2020
On a simplicial monoid whose underlying simplicial set is not a quasi-category
Ryo Horiuchi
It is well known that the underlying simplicial set of any simplicial group is a Kan complex. Roughly speaking, Kan complex is an infinite-dimensional analogue of groupoid, and the…