{"id":13993174,"url":"https://github.com/b-mehta/topos","last_synced_at":"2025-10-27T15:03:34.905Z","repository":{"id":90565521,"uuid":"240943034","full_name":"b-mehta/topos","owner":"b-mehta","description":"Topos theory in lean","archived":false,"fork":false,"pushed_at":"2021-01-06T04:29:03.000Z","size":3552,"stargazers_count":56,"open_issues_count":8,"forks_count":2,"subscribers_count":9,"default_branch":"master","last_synced_at":"2024-11-28T23:31:28.451Z","etag":null,"topics":["leanprover","topos-theory"],"latest_commit_sha":null,"homepage":null,"language":"Lean","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/b-mehta.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,"roadmap":null,"authors":null}},"created_at":"2020-02-16T18:27:48.000Z","updated_at":"2024-10-29T23:29:48.000Z","dependencies_parsed_at":null,"dependency_job_id":"a638ba3e-350e-4340-9df2-b63ffbe960b2","html_url":"https://github.com/b-mehta/topos","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/b-mehta%2Ftopos","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/b-mehta%2Ftopos/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/b-mehta%2Ftopos/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/b-mehta%2Ftopos/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/b-mehta","download_url":"https://codeload.github.com/b-mehta/topos/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":227143403,"owners_count":17737153,"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":["leanprover","topos-theory"],"created_at":"2024-08-09T14:02:15.590Z","updated_at":"2025-10-27T15:03:34.833Z","avatar_url":"https://github.com/b-mehta.png","language":"Lean","funding_links":[],"categories":["Lean"],"sub_categories":[],"readme":"![.github/workflows/main.yml](https://github.com/b-mehta/topos/workflows/.github/workflows/main.yml/badge.svg)\n\n# Topos theory for Lean\n\nThis repository contains formal verification of results in Topos Theory, drawing from \"Sheaves in Geometry and Logic\" and \"Sketches of an Elephant\". \n\n## What's here?\n- Cartesian closed categories\n- Sieves and grothendieck topologies including the open set topology\n- (Trunc) construction of finite products from binary products and terminal\n- Locally cartesian closed categories and epi-mono factorisations\n- Many lemmas about pullbacks (for instance the pasting lemma)\n- Skeleton of a category (assuming choice)\n- Subobject category\n- Subobject classifiers and power objects\n- Reflexive monadicity theorem\n- (Internal) Beck-Chevalley and Pare's theorem\n- Definition of a topos\n- Every topos is finitely cocomplete\n- Local cartesian closure of toposes and Fundamental Theorem of Topos Theory\n- Lawvere-Tierney topologies and sheaves\n- Sheafification of LT topologies\n- Proof that Lawvere-Tierney topologies generalise Grothendieck topologies\n\n## What's coming soon?\n- Proof that category of coalgebras for a comonad form a topos\n- Logical functors\n- Logic internal to a topos\n- Natural number objects\n\n## What might be coming?\n- Geometric morphisms\n- Filter/quotient construction on a topos\n- ETCS\n- The construction of the Cohen topos to show ZF doesn't prove CH\n- The construction of a topos to show ZF doesn't prove AC\n- A topos in which every function R -\u003e R is continuous\n- Giraud's theorem\n- Classifying toposes\n\n## Build Instructions\n\nEITHER:\n[Install lean and leanproject](https://leanprover-community.github.io/get_started.html#regular-install).\n\nOR:\nIf you have docker, spin up an instance of the `edayers/lean` image (or build your own using the provided Dockerfile).\n\nFINALLY:\nrun\n``` sh\nleanproject get b-mehta/topos\nleanproject build\n```\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fb-mehta%2Ftopos","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fb-mehta%2Ftopos","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fb-mehta%2Ftopos/lists"}