2 citations · 3 across the 12 of their papers we have counts for
14 papers
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…
Generalized Inverses of Quantum Channels: a categorical perspective
Robin Cockett, Jean-Simon Pacaud Lemay, Priyaa Varshinee Srinivasan
A quantum channel is defined as being completely positive (CP) and trace preserving (TP). While not every quantum channel is invertible or reversible, every quantum channel admits…
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…
Reverse Faà di Bruno's Formula for Cartesian Reverse Differential Categories
Aaron Biggin, Jean-Simon Pacaud Lemay
Reverse differentiation is an essential operation for automatic differentiation. Cartesian reverse differential categories axiomatize reverse differentiation in a categorical frame…
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…
Important Classes of Morphisms and the Relative Cotangent Sequence in Tangent Categories
Jean-Simon Pacaud Lemay, Geoff Vooys
In this paper we provide a deep and systematic study of what it means to be an immersion, a submersion, a local diffeomorphism, and unramified in a tangent category. We also give a…
Representable tangent structures for affine schemes
Marcello Lanfranchi, Jean-Simon Pacaud Lemay
The category of affine schemes is a tangent category whose tangent bundle functor is induced by Kähler differentials, providing a direct link between algebraic geometry and tangent…
A Tangent Category Perspective on Connections in Algebraic Geometry
G. S. H. Cruttwell, Jean-Simon Pacaud Lemay, Elias Vandenberg
There is an abstract notion of connection in any tangent category. In this paper, we show that when applied to the tangent category of affine schemes, this recreates the classical…
Drazin Inverses in Categories
Robin Cockett, Jean-Simon Pacaud Lemay, Priyaa Varshinee Srinivasan
Drazin inverses are a fundamental algebraic structure which have been extensively deployed in semigroup theory, ring theory, and matrix theory. Drazin inverses can also be defined…
Tensor-restriction categories
C. Heunen, J. S. Pacaud Lemay
Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic n…
Convenient Antiderivatives For Differential Linear Categories
Jean-Simon Pacaud Lemay
Differential categories axiomatize the basics of differentiation and provide categorical models of differential linear logic. A differential category is said to have antiderivative…