22 citations · 63 across the 24 of their papers we have counts for
5 papers · 1 filter
Differential equations in a tangent category I: Complete vector fields, flows, and exponentials
J. R. B. Cockett, G. S. H. Cruttwell, J. -S. P. Lemay
This paper describes how to define and work with differential equations in the abstract setting of tangent categories. The key notion is that of a curve object which is, for differ…
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…