https://github.com/unimath/grpdhits
https://github.com/unimath/grpdhits
Last synced: 11 months ago
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- Host: GitHub
- URL: https://github.com/unimath/grpdhits
- Owner: UniMath
- Created: 2019-08-16T14:43:36.000Z (over 6 years ago)
- Default Branch: master
- Last Pushed: 2024-02-08T13:00:00.000Z (about 2 years ago)
- Last Synced: 2025-03-25T14:44:37.924Z (12 months ago)
- Language: Coq
- Size: 943 KB
- Stars: 7
- Watchers: 7
- Forks: 4
- Open Issues: 1
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Metadata Files:
- Readme: README.md
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README
# Constructing Higher Inductive Types as Groupoid Quotients
We show that all finitary 1-truncated higher inductive types can be constructed with propositional truncations, set quotients, and the groupoid quotient. We formalize a notion of signature for HITs and we show that each signature gives rise to a bicategory of algebras in 1-types and in groupoids. Then we show that biinitial objects in the bicategory of algebras in 1-types satisfy the induction and we construct a biadjunction between thes two bicategories of algebras. We finish up by constructing a biinitial object in the bicategory of algebras in groupoids.
# Installation
- Make sure to have UniMath (https://github.com/UniMath/UniMath) installed
- coq_makefile -f _CoqProject -o Makefile
- make
To decrease the compilation time, it is suggested to do `make -j 3` instead of `make`.