ℹ️ This project originated as a fork of https://github.com/emilyriehl/yoneda.
This is a formalization library for simplicial Homotopy Type Theory (sHoTT) with the aim of proving resulting in synthetic ∞-category theory, starting with the results from the following papers:
- "A type theory for synthetic ∞-categories" [1]
- "Synthetic fibered (∞,1)-category theory" [2]
- "Limits and colimits of synthetic ∞-categories" [3]
This formalization project follows the philosophy layed out in the article "Could ∞-category theory be taught to undergraduates?" [4].
The formalizations are implemented using
rzk, an experimental proof assistant for a
variant of type theory with shapes. See the list of contributors at
src/CONTRIBUTORS.md.
The formalizations can be viewed as markdown files rendered at rzk-lang.github.io/sHoTT/ using syntax highlighting supplied by MkDocs plugin for rzk.
Install the
rzk proof
assistant. Then run the following command from the root of this repository:
rzk typecheck src/hott/* src/simplicial-hott/*-
Emily Riehl & Michael Shulman. A type theory for synthetic ∞-categories. Higher Structures 1(1), 147-224. 2017. https://arxiv.org/abs/1705.07442
-
Ulrik Buchholtz and Jonathan Weinberger. 2023. Synthetic fibered (∞, 1)-category theory. Higher Structures 7 (2023), 74–165. Issue 1. https://doi.org/10.21136/HS.2023.04
-
César Bardomiano Martínez. Limits and colimits of synthetic ∞-categories. 1-33, 2022. https://arxiv.org/abs/2202.12386
-
Emily Riehl. Could ∞-category theory be taught to undergraduates? Notices of the AMS. May 2023. https://www.ams.org/journals/notices/202305/noti2692/noti2692.html