univalent foundations program
E860090
The univalent foundations program is a research initiative that redefines the foundations of mathematics using homotopy type theory, emphasizing computationally verifiable proofs and new connections between logic, topology, and category theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| univalent foundations program canonical | 1 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
foundations of mathematics program
ⓘ
mathematical research initiative ⓘ research program ⓘ |
| aimsTo |
integrate homotopical ideas into foundations of mathematics
ⓘ
provide a new foundation for mathematics using type theory ⓘ redefine the foundations of mathematics ⓘ support computer-verified mathematical proofs ⓘ |
| basedOn |
homotopy type theory
NERFINISHED
ⓘ
univalence axiom NERFINISHED ⓘ |
| contrastsWith |
Zermelo–Fraenkel set theory
NERFINISHED
ⓘ
set-theoretic foundations ⓘ |
| coreConcept |
equivalences as identities
ⓘ
higher-dimensional structure of equality ⓘ types as spaces ⓘ univalence axiom NERFINISHED ⓘ |
| emphasizes |
computationally verifiable proofs
ⓘ
connections between logic and category theory ⓘ connections between logic and topology ⓘ connections between topology and category theory ⓘ formalization of mathematics in proof assistants ⓘ |
| field |
algebraic topology
ⓘ
category theory ⓘ foundations of mathematics ⓘ homotopy type theory ⓘ mathematical logic ⓘ type theory ⓘ |
| focusesOn |
formal verification of mathematics
ⓘ
machine-checked proofs ⓘ |
| influencedBy |
constructive mathematics
ⓘ
higher category theory ⓘ homotopy theory ⓘ |
| proposes |
equivalences as identities between structures
ⓘ
types as fundamental objects of mathematics ⓘ |
| relatedTo |
Agda
NERFINISHED
ⓘ
Coq NERFINISHED ⓘ HoTT/UF community NERFINISHED ⓘ Lean theorem prover NERFINISHED ⓘ proof assistants ⓘ |
| supports |
formalization of algebra
ⓘ
formalization of category theory ⓘ formalization of higher category theory ⓘ formalization of homotopy theory ⓘ formalization of topology ⓘ |
| timePeriod | 21st century ⓘ |
| uses |
dependent type theory
ⓘ
higher inductive types ⓘ identity types as paths ⓘ intensional type theory ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.