11 papers · 1 filter
Characterizing (Co)Free Dagger Categories
Jean-Simon Pacaud Lemay
For any category, there exists both a free dagger category and a cofree dagger category over it. A natural question to ask is: given a dagger category, how can we tell if it is fre…
Override and Update in Restriction Categories
Jean-Simon Pacaud Lemay, Chad Nester
We study the override and update operators on partial functions from the perspective of restriction categories. We propose a definition of override restriction categories, in which…
Local categories: a new framework for partiality
Marcello Lanfranchi, Jean-Simon Pacaud Lemay
Restriction categories provide a categorical framework for partiality. In this paper, we introduce three new categorical theories for partiality: local categories, partial categori…
From Abelianization to Tangent Categories
Sacha Ikonicoff, Jean-Simon Pacaud Lemay, Tim Van der Linden
A tangent category is a category with an endofunctor, called the tangent bundle functor, which is equipped with various natural transformations that capture essential properties of…
Cartesian Linearly Distributive Categories: Revisited
Rose Kudzman-Blais, Jean-Simon Pacaud Lemay
Linearly distributive categories (LDC) were introduced by Cockett and Seely to provide alternative categorical semantics for multiplicative linear logic. In contrast to Barr's -…
Dagger categories of relations: The equivalence of dilatory dagger categories and epi-regular independence categories
Matthew Di Meglio, Chris Heunen, Jean-Simon Pacaud Lemay +2
Several categories look like categories of relations, but do not fit the established theory of relations in regular categories. They include the category of surjective multivalued…