1 citations · 1 across the 1 of their papers we have counts for
6 papers
Why FHilb is Not an Interesting (Co)Differential Category
Jean-Simon Pacaud Lemay
Differential categories provide an axiomatization of the basics of differentiation and categorical models of differential linear logic. As differentiation is an important tool thro…
Cartesian Difference Categories: Extended Report
Mario Alvarez-Picallo, Jean-Simon Pacaud Lemay
Cartesian differential categories are categories equipped with a differential combinator which axiomatizes the directional derivative. Important models of Cartesian differential ca…
Exponential Functions in Cartesian Differential Categories
Jean-Simon Pacaud Lemay
In this paper, we introduce differential exponential maps in Cartesian differential categories, which generalizes the exponential function from classical differential calculu…
Reverse derivative categories
Robin Cockett, Geoffrey Cruttwell, Jonathan Gallagher +4
The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivativ…
Tangent Categories from the Coalgebras of Differential Categories
Robin Cockett, Jean-Simon Pacaud Lemay, Rory B. B. Lucyshyn-Wright
Following the pattern from linear logic, the coKleisli category of a differential category is a Cartesian differential category. What then is the coEilenberg-Moore category of a di…
Integral and differential structure on the free -ring modality
G. S. H. Cruttwell, J. -S. P. Lemay, R. B. B. Lucyshyn-Wright
Integral categories were recently developed as a counterpart to differential categories. In particular, integral categories come equipped with an integration operator, known as an…