{"id":26070243,"url":"https://github.com/unimath/largecatmodules","last_synced_at":"2025-10-17T13:20:26.600Z","repository":{"id":13842141,"uuid":"75078674","full_name":"UniMath/largecatmodules","owner":"UniMath","description":"Large category of modules over monads on top of UniMaths and Display category","archived":false,"fork":false,"pushed_at":"2024-09-06T11:55:20.000Z","size":983,"stargazers_count":12,"open_issues_count":7,"forks_count":8,"subscribers_count":6,"default_branch":"master","last_synced_at":"2025-03-25T14:44:37.521Z","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,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2016-11-29T12:19:39.000Z","updated_at":"2025-03-04T05:08:34.000Z","dependencies_parsed_at":"2024-06-12T13:40:51.806Z","dependency_job_id":"a5420715-eda1-4255-9e53-37f5e9ac9417","html_url":"https://github.com/UniMath/largecatmodules","commit_stats":null,"previous_names":[],"tags_count":1,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/UniMath%2Flargecatmodules","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/UniMath%2Flargecatmodules/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/UniMath%2Flargecatmodules/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/UniMath%2Flargecatmodules/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/UniMath","download_url":"https://codeload.github.com/UniMath/largecatmodules/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":248464172,"owners_count":21108233,"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":"2025-03-08T23:07:42.196Z","updated_at":"2025-10-17T13:20:26.532Z","avatar_url":"https://github.com/UniMath.png","language":"Coq","funding_links":[],"categories":[],"sub_categories":[],"readme":"# largecatmodules\nLarge category of modules over monads on top of UniMath.\nSignatures for higher order syntax.\n\nPreliminaries are in the subfolder Modules/Prelims\n1-Signature related proofs are in the subfolder Modules/Signatures\n2-Signature related proofs are in the subfolder Modules/SoftEquations\n\nRequirement: the UniMath library (installed with `$ make install`)\n\nTo compile (Coq 8.9.0): `$ make`\n\n\n\n# List of some important formalized propositions and definitions\n\nThe file `SoftEquations/Summary` gives a summary of main formalized propositions and definitions\nfor 2-signatures and elementary equations.\n\nFor the rest:\n\n- Definition of signatures and their actions : `Signatures/Signature`\n- Representability of presentable signatures : `Signatures/PresentableSignature`\n- Representability of the codomain epimorphic morphism of signature : `Signatures/EpiSigRepresentability`\n- Adjunction in the category of modules over a specific monad R  on Set\n          Hom(M x R', N) ~ Hom(M , N') : `Prelims/derivadj`\n          \n\n- A coproduct of presentable  signatures is presentable : `Signatures/PresentableSignatureCoproducts` \n- The binproduct of a presentable  signature with the tautological signature is\n     presentable : `Signatures/PresentableSignatureBinProdR` \n- pointwise limits and colimits of modules : `Prelims/LModuleColims`\n- pointwise limits and colimits of signatures : `Signatures/SignaturesColims`\n- quotient monad : `Prelims/quotientmonad`\n- Epimorphisms of signatures are pointwise epimorphisms : `Signatures/EpiArePointwise`\n- Modularity in the context of a fibration : `Prelims/FibrationInitialPushout`\n- Modularity in the specific context of signatures and their models : `Signatures/Modularity`\n          \nThe fact that algebraic signatures are effective is already proved in\na different setting in the Heterogeneous Substitution System package of UniMath.\nThe adaptation to our setting is carried out in the files : `Signatures/SigWithStrengthToSignature`,\n`Signatures/HssInitialModel` and `Signatures/BindingSig`.\n\n# Summary of files\nBy folder\n\n## Prelims\n\n    \n- `quotientmonad`, `quotientmonadslice` : the quotient monad construction\n- `FibrationInitialPushout` : modularity in the context of a fibration\n\n- `DerivationIsFunctorial` : Proof that derivation of modules is functorial\n- `derivadj` : Adjunction in the category of modules over a specific monad R on Set\n          Hom(M x R', N) ~ Hom(M , N') \n\n- `LModulesFibration` : fibration of left modules over monads\n- `LModulesColims` : limits and colimits of modules\n- `LModulesBinProducts`, `LModulesCoproducts` : direct definition of some particular\n    colimits/limits of modules\n\n- `PushoutsFromCoeqBinCoproducts` : Pushouts from coequalizers and binary coproducts\n- `FaithfulFibrationEqualizer` : Faithful fibrations lift coequalizers\n- `Opfibration` : definition of opfibrations (adapted from the definition of fibrations in UniMath)\n\n- `BinCoproductComplements`, `BinProductComplements` , `CoproductsComplements`, `EpiComplements`\n  `LModulesComplements`, `SetCatComplements`, `lib` : various complements\n\n## Signatures\nEverything here is about 1-signatures\n\n- `Signature` : definition of signatures and the displayed category of models \n- `ModelCat` : direct definition of the category of models of a signature\n- `EpiSigRepresentability` : proof of the technical lemma : epimorphisms of signatures preserves\n       representability\n- `PresentableSignatures` : presentable signatures are effective.\n- `Modularity` : Modularity in the specific context of signatures and their models\n- `quotientrep` : quotient model construction\n\n- `HssInitialModel`, `BindingSig` : adaptation of the proof in UniMath of initiality for strengthened signatures\n       (in particular, for binding or algebraic signatures)\n- `PreservesEpi` : Epi-signatures \n\n- `EpiArePointwise` : epimorphisms of signatures are pointwise epimorphisms\n- `PresentableSignatureCoproducts` : a coproduct of presentable  signatures is presentable.\n- `PresentableSignatureBinProdR` : if `a` is presentable, then so is the product of `a` with\n       the tautological signature \n- `SignaturesColims` : colimits of  signatures\n- `SignatureBinproducts` : direct definition of bin products of  signatures\n- `SignatureCoproduct` : direct definition of coproducts of  signatures\n- `SignatureDerivation` : derivation of signatures\n\n- `SigWithStrengthToSignature` : Functor between signatures with strength\n       and our  signatures.\n- `HssSignatureCommutation` : Somme commutation rules between colimits/limits and the \n       functor between signatures with strength and our\n       signatures\n       \n## SoftEquations\nThis folder is about 2-signatures and elementary equations\n\n- `Summary` : summary of main propositions and definitions\n\n- `SignatureOver` : category of Σ-modules\n- `CatOfTwoSignatures` : category of 2-signatures, fibration of 2-models over it\n- `Equation` : equations, and category of models satisfying those equations\n- `quotientequation` : quotient model satisfying the equations\n- `quotientrepslice` : more general quotient model construction\n- `AdjunctionEquationRep` : algebraic 2-signatures are effective and related proofs\n- `Modularity` : modularity in the specific context of 2-signatures and their models\n\n- `Examples/LCBetaEta` : example of the lambda calculus modulo beta eta\n- `SignatureOverAsFiber` : (unused) alternative definition of Σ-modules as a displayed category\n        over the category of 1-signatures\n- `SignatureOverBinproducts` : binary products of Σ-modules\n- `SignatureOverDerivation` : derivative of a Σ-module\n- `BindingSig` : complements about algebraic 1-signatures\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Funimath%2Flargecatmodules","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Funimath%2Flargecatmodules","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Funimath%2Flargecatmodules/lists"}