4 papers
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…
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…
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…