https://github.com/rzk-lang/sHoTT
Formalisations for simplicial HoTT and synthetic ∞-categories.
https://github.com/rzk-lang/sHoTT
Last synced: 7 months ago
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Formalisations for simplicial HoTT and synthetic ∞-categories.
- Host: GitHub
- URL: https://github.com/rzk-lang/sHoTT
- Owner: rzk-lang
- Created: 2023-04-13T17:43:23.000Z (about 2 years ago)
- Default Branch: main
- Last Pushed: 2023-12-15T01:37:08.000Z (over 1 year ago)
- Last Synced: 2024-02-17T15:32:23.366Z (over 1 year ago)
- Language: Markdown
- Homepage: https://rzk-lang.github.io/sHoTT/
- Size: 11.7 MB
- Stars: 33
- Watchers: 12
- Forks: 11
- Open Issues: 20
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# Simplicial HoTT and synthetic ∞-categories
[](https://github.com/rzk-lang/sHoTT/actions/workflows/rzk.yml)
[](https://github.com/rzk-lang/sHoTT/actions/workflows/mkdocs.yml)
> :information_source: 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](https://higher-structures.math.cas.cz/api/files/issues/Vol1Iss1/RiehlShulman)"
[1]
- "[Synthetic fibered (∞,1)-category theory](https://doi.org/10.21136/HS.2023.04)"
[2]
- "[Limits and colimits of synthetic ∞-categories](https://arxiv.org/abs/2202.12386)"
[3]
This formalization project follows the philosophy laid out in the article
"[Could ∞-category theory be taught to undergraduates?](https://www.ams.org/journals/notices/202305/noti2692/noti2692.html)"
[4].
The formalizations are implemented using
[`rzk`](https://github.com/rzk-lang/rzk), an experimental proof assistant for a
variant of type theory with shapes. See the list of contributors at
[`src/CONTRIBUTORS.md`](src/CONTRIBUTORS.md).
The formalizations can be viewed as markdown files rendered at
[rzk-lang.github.io/sHoTT/](https://rzk-lang.github.io/sHoTT/) using syntax
highlighting supplied by
[MkDocs plugin for Rzk](https://github.com/rzk-lang/mkdocs-plugin-rzk).
## Checking the formalisations locally
Install the
[`rzk`](https://rzk-lang.github.io/rzk/en/latest/getting-started/install/) proof
assistant. Then run the following command from the root of this repository:
```sh
rzk typecheck
```
Please also have a look at our [style guide](src/STYLEGUIDE.md) before
submitting your pull request.
# References
1. Emily Riehl & Michael Shulman. A type theory for synthetic ∞-categories.
Higher Structures 1(1), 147-224. 2017. https://arxiv.org/abs/1705.07442
2. 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
3. César Bardomiano Martínez. Limits and colimits of synthetic ∞-categories.
1-33, 2022. https://arxiv.org/abs/2202.12386
4. 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