5 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, MartÃn 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…
Constructive Ordinal Exponentiation
Tom de Jong, Nicolai Kraus, Fredrik Nordvall Forsberg +1
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the con…
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…