7 papers
Generalized Decidability via Brouwer Trees
Tom de Jong, Nicolai Kraus, Aref Mohammadzadeh +1
In the setting of constructive mathematics, we suggest and study a framework for decidability of properties, which allows for finer distinctions than just "decidable, semidecidable…
The Leibniz adjunction in homotopy type theory, with an application to simplicial type theory
Tom de Jong, Nicolai Kraus, Axel Ljungström
Simplicial type theory extends homotopy type theory and equips types with a notion of directed morphisms. A Segal type is defined to be a type in which these directed morphisms can…
Examples and counterexamples of injective types
Tom de Jong, Martín Hötzel Escardó
It is known that, in univalent mathematics, type universes, the type of -types in a universe, reflective subuniverses, and the underlying type of any algebra of the lifting mona…
A study of Kock's fat Delta
Tom de Jong, Nicolai Kraus, Simona Paoli +1
Motivated by the study of weak identity structures in higher category theory we explore the fat Delta category, a modification of the simplex category introduced by J. Kock and pro…
Formalizing equivalences without tears
Tom de Jong
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…
Domain theory in univalent foundations I: Directed complete posets and Scott's
Tom de Jong
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 Voevodsk…