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

Taichi Uemura

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arXiv · 2410.17615

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

Taichi Uemura

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Abstract

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 inductive types is finitarily presentable. In particular, the initial $(\infty,1)$-category with higher inductive types exists. We prove a form of canonicity: the global section functor for the initial $(\infty,1)$-category with higher inductive types preserves higher inductive types.

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Taichi Uemura. 2024-10-23. Higher inductive types in $(\infty,1)$-categories. https://arxiv.org/abs/2410.17615

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