Statements (89)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:logic
|
| gptkbp:abbreviation |
gptkb:HoTT
|
| gptkbp:developedBy |
21st century
|
| gptkbp:field |
gptkb:logic
gptkb:mathematics computer science |
| gptkbp:hasConcept |
gptkb:synthetic_geometry
gptkb:Freudenthal_suspension_theorem gptkb:Blakers–Massey_theorem gptkb:Eilenberg–MacLane_spaces gptkb:synthetic_mathematics gptkb:van_Kampen_theorem gptkb:Hurewicz_theorem gptkb:Whitehead's_theorem transport suspension constructive logic colimits contractibility dependent types equivalence of types fiber sequences function extensionality higher groupoids homotopy levels n-types path induction pointed types propositional truncation propositions as types pushouts synthetic homotopy theory synthetic topology universe polymorphism spheres homotopy groups loop spaces groupoids coherence laws equivalences higher categories identity morphisms long exact sequences n-truncation path spaces set-truncation synthetic algebra synthetic algebraic topology synthetic analysis synthetic category theory synthetic combinatorics synthetic differential geometry synthetic group theory synthetic logic synthetic measure theory synthetic model theory synthetic number theory synthetic probability theory synthetic set theory truncation levels |
| https://www.w3.org/2000/01/rdf-schema#label |
Homotopy type theory
|
| gptkbp:influenced |
gptkb:univalent_foundations
proof assistants cubical type theory |
| gptkbp:influencedBy |
gptkb:Martin-Löf_type_theory
gptkb:category_theory homotopy theory |
| gptkbp:notableContributor |
gptkb:Steve_Awodey
gptkb:Vladimir_Voevodsky gptkb:Michael_Shulman gptkb:Andrej_Bauer gptkb:Peter_Aczel gptkb:Peter_Lumsdaine gptkb:Thorsten_Altenkirch |
| gptkbp:notableIdea |
higher inductive types
identity types univalence axiom |
| gptkbp:notablePublication |
gptkb:Homotopy_Type_Theory:_Univalent_Foundations_of_Mathematics
|
| gptkbp:relatedTo |
gptkb:logic
gptkb:category_theory gptkb:univalent_foundations homotopy theory |
| gptkbp:usedIn |
gptkb:logic
foundations of mathematics proof assistants formalization of mathematics |
| gptkbp:website |
https://homotopytypetheory.org/
|
| gptkbp:bfsParent |
gptkb:Curry–Howard_correspondence
|
| gptkbp:bfsLayer |
5
|