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 |
How this entity was disambiguated
This entity first appeared as the object of triple T10388496 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: univalent foundations program Context triple: [Vladimir Voevodsky, notableIdea, univalent foundations program]
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A.
Archive of Formal Proofs
The Archive of Formal Proofs is an online, peer-reviewed collection of machine-checked mathematical and computer science proofs formalized primarily in the Isabelle proof assistant.
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B.
Isabelle proof assistant
Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
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C.
Grothendieck universe
A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
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D.
Recent Synthetic Differential Geometry
"Recent Synthetic Differential Geometry" is a mathematical work by Herbert Busemann that develops differential geometry using synthetic, axiomatic methods rather than traditional analytic techniques.
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E.
Grothendieck toposes
Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: univalent foundations program Target entity description: 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.
-
A.
Archive of Formal Proofs
The Archive of Formal Proofs is an online, peer-reviewed collection of machine-checked mathematical and computer science proofs formalized primarily in the Isabelle proof assistant.
-
B.
Isabelle proof assistant
Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
-
C.
Grothendieck universe
A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
-
D.
Recent Synthetic Differential Geometry
"Recent Synthetic Differential Geometry" is a mathematical work by Herbert Busemann that develops differential geometry using synthetic, axiomatic methods rather than traditional analytic techniques.
-
E.
Grothendieck toposes
Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: univalent foundations program Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.