{"id":26070247,"url":"https://github.com/unimath/grpdhits","last_synced_at":"2025-04-11T18:51:00.628Z","repository":{"id":52186620,"uuid":"202744721","full_name":"UniMath/GrpdHITs","owner":"UniMath","description":null,"archived":false,"fork":false,"pushed_at":"2024-02-08T13:00:00.000Z","size":966,"stargazers_count":7,"open_issues_count":1,"forks_count":4,"subscribers_count":7,"default_branch":"master","last_synced_at":"2025-03-25T14:44:37.924Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Coq","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/UniMath.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null}},"created_at":"2019-08-16T14:43:36.000Z","updated_at":"2025-03-04T05:09:53.000Z","dependencies_parsed_at":"2022-08-24T02:10:54.397Z","dependency_job_id":null,"html_url":"https://github.com/UniMath/GrpdHITs","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/UniMath%2FGrpdHITs","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/UniMath%2FGrpdHITs/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/UniMath%2FGrpdHITs/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/UniMath%2FGrpdHITs/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/UniMath","download_url":"https://codeload.github.com/UniMath/GrpdHITs/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":248464180,"owners_count":21108236,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2025-03-08T23:07:43.269Z","updated_at":"2025-04-11T18:51:00.598Z","avatar_url":"https://github.com/UniMath.png","language":"Coq","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Constructing Higher Inductive Types as Groupoid Quotients\n\nWe 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.\n\n# Installation\n\n- Make sure to have UniMath (https://github.com/UniMath/UniMath) installed\n- coq_makefile -f _CoqProject -o Makefile\n- make\n\nTo decrease the compilation time, it is suggested to do `make -j 3` instead of `make`.","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Funimath%2Fgrpdhits","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Funimath%2Fgrpdhits","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Funimath%2Fgrpdhits/lists"}