4 papers
math.CT2026
Homotopy type theory as a language for diagrams of -logoses
Taichi Uemura
We show that certain diagrams of -logoses are reconstructed in homotopy type theory extended with some lex, accessible modalities, which enables us to use plain homotopy ty…
math.CT2025
Colimits in the -category of -topoi and étale morphisms
Taichi Uemura
We provide an alternative proof of Lurie's result that the wide subcategory of the -category of -topoi spanned by the étale morphisms is closed under small colimit…
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 -categories
Taichi Uemura
We propose a definition of higher inductive types in -categories with finite limits. We show that the -category of -categories with higher induc…