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pro vyhledávání: '"de Jong, Tom"'
Autor:
de Jong, Tom
This expository note describes two convenient techniques in the context of homotopy type theory for proving and formalizing that a given map is an equivalence. The first technique decomposes the map as a series of basic equivalences, while the second
Externí odkaz:
http://arxiv.org/abs/2408.11501
Autor:
de Jong, Tom
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive in the sen
Externí odkaz:
http://arxiv.org/abs/2407.06952
Autor:
de Jong, Tom, Escardó, Martín Hötzel
We develop the theory of continuous and algebraic domains in constructive and predicative univalent foundations, building upon our earlier work on basic domain theory in this setting. That we work predicatively means that we do not assume Voevodsky's
Externí odkaz:
http://arxiv.org/abs/2407.06956
We characterize the epimorphisms in homotopy type theory (HoTT) as the fiberwise acyclic maps and develop a type-theoretic treatment of acyclic maps and types in the context of synthetic homotopy theory as developed in univalent foundations. We prese
Externí odkaz:
http://arxiv.org/abs/2401.14106
Autor:
de Jong, Tom
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive in the sen
Externí odkaz:
http://arxiv.org/abs/2301.12405
Publikováno v:
38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2023
In constructive set theory, an ordinal is a hereditarily transitive set. In homotopy type theory (HoTT), an ordinal is a type with a transitive, wellfounded, and extensional binary relation. We show that the two definitions are equivalent if we use (
Externí odkaz:
http://arxiv.org/abs/2301.10696
Autor:
de Jong, Tom
Publikováno v:
EPTCS 351, 2021, pp. 134-151
Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness and a notion of sharp elements. Being apart is a positive formulation of being unequal,
Externí odkaz:
http://arxiv.org/abs/2112.14052
Autor:
de Jong, Tom, Escardó, Martín Hötzel
Publikováno v:
Logical Methods in Computer Science, Volume 19, Issue 2 (May 4, 2023) lmcs:8643
We investigate predicative aspects of constructive univalent foundations. By predicative and constructive, we respectively mean that we do not assume Voevodsky's propositional resizing axioms or excluded middle. Our work complements existing work on
Externí odkaz:
http://arxiv.org/abs/2111.00482
Autor:
de Jong, Tom
Publikováno v:
Mathematical Structures in Computer Science (2023) 1-32
Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness and a notion of sharp elements. Being apart is a positive formulation of being unequal,
Externí odkaz:
http://arxiv.org/abs/2106.05064
Autor:
de Jong, Tom, Escardó, Martín Hötzel
We investigate predicative aspects of order theory in constructive univalent foundations. By predicative and constructive, we respectively mean that we do not assume Voevodsky's propositional resizing axioms or excluded middle. Our work complements e
Externí odkaz:
http://arxiv.org/abs/2102.08812