7 citations · 11 across the 4 of their papers we have counts for
9 papers · 1 filter
Type Theory with Single Substitutions
Ambrus Kaposi, Szumi Xie
Type theory can be described as a generalised algebraic theory. This automatically gives a notion of model and the existence of the syntax as the initial model, which is a quotient…
The Groupoid-Syntax of Type Theory is a Set
Thorsten Altenkirch, Ambrus Kaposi, Szumi Xie
Categories with families (CwFs) have been used to define the semantics of type theory in type theory. In the setting of Homotopy Type Theory (HoTT), one of the limitations of the t…
Internal parametricity, without an interval
Thorsten Altenkirch, Yorgo Chamoun, Ambrus Kaposi +1
Parametricity is a property of the syntax of type theory implying, e.g., that there is only one function having the type of the polymorphic identity function. Parametricity is usua…
For the Metatheory of Type Theory, Internal Sconing Is Enough
Rafaël Bocquet, Ambrus Kaposi, Christian Sattler
Metatheorems about type theories are often proven by interpreting the syntax into models constructed using categorical gluing. We propose to use only sconing (gluing along a global…
Relative induction principles for type theories
Rafaël Bocquet, Ambrus Kaposi, Christian Sattler
We present new induction principles for the syntax of dependent type theories, which we call relative induction principles. The result of the induction principle relative to a func…
Large and Infinitary Quotient Inductive-Inductive Types
András Kovács, Ambrus Kaposi
Quotient inductive-inductive types (QIITs) are generalized inductive types which allow sorts to be indexed over previously declared sorts, and allow usage of equality constructors.…