Statements (100)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:logic
|
| gptkbp:application |
foundations of mathematics
proof assistants formalization of mathematics |
| gptkbp:developedBy |
21st century
|
| gptkbp:field |
gptkb:logic
gptkb:mathematics computer science |
| gptkbp:hasConcept |
gptkb:Agda
gptkb:Coq gptkb:Lean gptkb:Cubical_Agda gptkb:Cubical_Type_Theory gptkb:Quillen_model_structure gptkb:constructive_set_theory transport constructive logic formal verification proof assistants coherence fibrations limits Kan complexes coequalizers cofibrations colimits computer formalization contractibility cubical type theory dependent product dependent sum dependent types equalizers equivalence equivalence of types fiber sequences function extensionality function types h-groupoids h-propositions h-sets higher groupoids higher inductive types higher paths homotopy fiber homotopy levels identity elimination identity types initial types internal language judgmental equality loop space model categories n-types path induction path space pointed types product types proof irrelevance propositional equality propositional truncation propositions as types pullbacks pushouts semantic identity simplicial sets sum types syntactic identity synthetic homotopy theory synthetic reasoning synthetic topology terminal types truncation type universes univalence axiom universe polymorphism |
| https://www.w3.org/2000/01/rdf-schema#label |
homotopy type theory
|
| gptkbp:influenced |
gptkb:logic
gptkb:univalent_foundations computer-assisted proof |
| gptkbp:influencedBy |
gptkb:Martin-Löf_type_theory
gptkb:category_theory homotopy theory |
| gptkbp:notableContributor |
gptkb:Michael_Warren
gptkb:Steve_Awodey gptkb:Vladimir_Voevodsky gptkb:Andrej_Bauer gptkb:Peter_Lumsdaine gptkb:Thorsten_Altenkirch |
| gptkbp:notableWork |
gptkb:Homotopy_Type_Theory:_Univalent_Foundations_of_Mathematics
|
| gptkbp:publicationYear |
2013
|
| gptkbp:publishedBy |
gptkb:The_Univalent_Foundations_Program
|
| gptkbp:relatedTo |
gptkb:logic
gptkb:category_theory gptkb:univalent_foundations homotopy theory |
| gptkbp:uses |
higher inductive types
univalence axiom |
| gptkbp:bfsParent |
gptkb:logic
|
| gptkbp:bfsLayer |
4
|