1 citations · 1 across the 2 of their papers we have counts for
7 papers
Measuring data types
Lukas Mulder, Paige Randall North, Maximilien Péroux
In this article, we combine Sweedler's classic theory of measuring coalgebras -- by which -algebras are enriched in -coalgebras for a field -- with the theory of W-types…
Comparing semantic frameworks for dependently-sorted algebraic theories
Benedikt Ahrens, Peter LeFanu Lumsdaine, Paige Randall North
Algebraic theories with dependency between sorts form the structural core of Martin-Löf type theory and similar systems. Their denotational semantics are typically studied using c…
Functoriality of Enriched Data Types
Lukas Mulder, Paige Randall North, Maximilien Péroux
In previous work, categories of algebras of endofunctors were shown to be enriched in categories of coalgebras of the same endofunctor, and the extra structure of that enrichment w…
Directed type theory, with a twist
Fernando Rafael Chu Rivera, Paige Randall North
In recent years, Homotopy Type Theory (HoTT) has had great success both as a foundation of mathematics and as internal language to reason about -groupoids (a.k.a. spaces).…
Categorical Diffusion of Weighted Lattices
Robert Ghrist, Miguel Lopez, Paige Randall North +1
We introduce a categorical formalization of diffusion processes for network-structured data, motivated by applications in data science and information dynamics. At the heart of our…
From Semantics to Syntax: A Type Theory for Comprehension Categories
Niyousha Najmaei, Niels van der Weide, Benedikt Ahrens +1
Recent models of intensional type theory have been constructed in algebraic weak factorization systems (AWFSs). AWFSs give rise to comprehension categories that feature non-trivial…