21 citations · 25 across the 3 of their papers we have counts for
6 papers
Double Fibrations
Geoffrey Cruttwell, Michael Lambert, Dorette Pronk +1
This paper defines double fibrations (fibrations of double categories) and describes their key examples and properties. In particular, it shows how double fibrations relate to exis…
Categorical semantics of a simple differential programming language
Geoffrey Cruttwell, Jonathan Gallagher, Dorette Pronk
With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been t…
Latent Fibrations: Fibrations for Categories of Partial Maps
Robin Cockett, Geoff Cruttwell, Jonathan Gallagher +1
Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. The paper initiates the…
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…
Affine geometric spaces in tangent categories
R. F. Blute, G. S. H. Cruttwell, R. B. B. Lucyshyn-Wright
We continue the program of structural differential geometry that begins with the notion of a tangent category, an axiomatization of structural aspects of the tangent functor on the…
Differential restriction categories
J. R. B. Cockett, G. S. H. Cruttwell, J. D. Gallagher
We combine two recent ideas: cartesian differential categories, and restriction categories. The result is a new structure which axiomatizes the category of smooth maps defined on o…