72 citations · 159 across the 26 of their papers we have counts for
5 papers · 1 filter
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…
Univalent foundations and the equivalence principle
Benedikt Ahrens, Paige Randall North
In this paper, we explore the 'equivalence principle' (EP): roughly, statements about mathematical objects should be invariant under an appropriate notion of equivalence for the ki…
Bicategorical type theory: semantics and syntax
Benedikt Ahrens, Paige Randall North, Niels van der Weide
We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is…
The solutions to single-variable polynomials, implemented and verified in Lean
Nicholas Dyson, Benedikt Ahrens, Jacopo Emmenegger
In this work, we describe our experience in learning the use of a computer proof assistant - specifically, Lean - from scratch, through proving formulae for the solutions of polyno…