Taichi Uemura

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20182025

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5 papers · 1 filter

math.CT2025

Colimits in the $\infty$ -category of $\infty$ -topoi and étale morphisms

Taichi Uemura

We provide an alternative proof of Lurie's result that the wide subcategory of the $\infty$ -category of $\infty$ -topoi spanned by the étale morphisms is closed under small colimits…

math.CT2025

An elementary definition of opetopic sets

Taichi Uemura

We propose elementary definitions of opetopes and opetopic sets. We directly define opetopic sets by a simple structure and several axioms. Opetopes are then opetopic sets satisfyi…

math.CT2024

Higher inductive types in $(\infty, 1)$ -categories

Taichi Uemura

We propose a definition of higher inductive types in $(\infty, 1)$ -categories with finite limits. We show that the $(\infty, 1)$ -category of $(\infty, 1)$ -categories with higher induc…

math.CT2022

$\infty$ -type theories

Hoang Kim Nguyen, Taichi Uemura

We introduce $\infty$ -type theories as an $\infty$ -categorical generalization of the categorical definition of type theories introduced by the second named author. We establish ana…

math.CT2019

$W$ -Types in Categories of Coalgebras

Taichi Uemura

We construct $W$ -types in the category of coalgebras for a cartesian comonad. It generalizes the constructions of $W$ -types in presheaf toposes and gluing toposes.

Colimits in the ∞-category of ∞-topoi and étale morphisms

An elementary definition of opetopic sets

Higher inductive types in (∞,1)-categories

∞-type theories

W-Types in Categories of Coalgebras

Colimits in the $\infty$ -category of $\infty$ -topoi and étale morphisms

Higher inductive types in $(\infty, 1)$ -categories

$\infty$ -type theories

$W$ -Types in Categories of Coalgebras