6 papers
The Rezk Completion for Elementary Topoi
Kobe Wullaert, Niels van der Weide
The development of category theory in univalent foundations and the formalization thereof is an active field of research. Categories in that setting are often assumed to be univale…
Scott's Representation Theorem and the Univalent Karoubi Envelope
Arnoud van der Leer, Kobe Wullaert, Benedikt Ahrens
Lambek and Scott constructed a correspondence between simply-typed lambda calculi and Cartesian closed categories. Scott's Representation Theorem is a cousin to this result for unt…
Substitution for Non-Wellfounded Syntax with Binders through Monoidal Categories
Ralph Matthes, Kobe Wullaert, Benedikt Ahrens
We describe a generic construction of non-wellfounded syntax involving variable binding and its monadic substitution operation. Our construction of the syntax and its substitution…
Formalizing Monoidal Categories and Actions for Syntax with Binders
Benedikt Ahrens, Ralph Matthes, Kobe Wullaert
We discuss some aspects of our work on the mechanization of syntax and semantics in the UniMath library, based on the proof assistant Coq. We focus on experiences where Coq (as a t…
Univalent Monoidal Categories
Kobe Wullaert, Ralph Matthes, Benedikt Ahrens
Univalent categories constitute a well-behaved and useful notion of category in univalent foundations. The notion of univalence has subsequently been generalized to bicategories an…
Category Theory for Programming
Benedikt Ahrens, Kobe Wullaert
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we stud…