homotopy type theory
E1041770
branch of mathematical logic
foundational framework for mathematics
mathematics book
research area in type theory
Homotopy type theory is a branch of mathematical logic and foundations that interprets types as spaces and equalities as paths, connecting type theory with homotopy theory and higher category theory.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Homotopy Type Theory: Univalent Foundations of Mathematics | 0 |
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
branch of mathematical logic
ⓘ
foundational framework for mathematics ⓘ mathematics book ⓘ research area in type theory ⓘ |
| about | homotopy type theory NERFINISHED ⓘ |
| aimsToProvide | new foundations for mathematics ⓘ |
| associatedWith |
Institute for Advanced Study
NERFINISHED
ⓘ
Univalent Foundations program NERFINISHED ⓘ |
| basedOn | Martin-Löf dependent type theory NERFINISHED ⓘ |
| coreConcept |
higher inductive types
ⓘ
homotopy levels ⓘ identity types ⓘ n-types ⓘ path induction ⓘ truncation levels ⓘ univalence axiom NERFINISHED ⓘ |
| developedIn | 21st century ⓘ |
| fieldOfStudy |
higher category theory
ⓘ
homotopy theory ⓘ type theory ⓘ |
| hasAxiom | univalence axiom ⓘ |
| hasModelIn |
Kan complexes
ⓘ
simplicial sets ⓘ ∞-groupoids ⓘ |
| hasProperty |
internalizes homotopical reasoning in type theory
ⓘ
supports higher-dimensional algebraic structures ⓘ treats isomorphic structures as equal via univalence ⓘ |
| implementedIn |
Agda
NERFINISHED
ⓘ
Coq NERFINISHED ⓘ Cubical Agda NERFINISHED ⓘ Lean NERFINISHED ⓘ cubical type theory ⓘ |
| influencedBy |
constructive type theory
ⓘ
higher category theory ⓘ homotopy theory NERFINISHED ⓘ |
| influences |
computer-assisted theorem proving
ⓘ
formalized mathematics ⓘ univalent foundations ⓘ |
| interprets |
equalities as paths
ⓘ
higher equalities as homotopies between paths ⓘ terms as points in spaces ⓘ types as spaces ⓘ |
| notablePublication | Homotopy Type Theory: Univalent Foundations of Mathematics NERFINISHED ⓘ |
| relatesTo |
higher categories
ⓘ
model categories ⓘ simplicial sets ⓘ ∞-groupoids ⓘ |
| supports |
computer-checked proofs
ⓘ
constructive mathematics ⓘ |
| usedIn | proof assistants ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.