590 citations
- University of GlasgowGB65 papers
- George Washington UniversityUS64 papers
- Johannes Gutenberg University MainzDE59 papers
- University of BonnDE58 papers
- University of BaselCH56 papers
- Kent State UniversityUS55 papers
- Istituto Nazionale di Fisica Nucleare, Sezione di PaviaIT54 papers
- Institute for Nuclear ResearchRU51 papers
- Ruđer Bošković InstituteHR50 papers
- University of California, Los AngelesUS50 papers
- University of EdinburghGB49 papers
- P.N. Lebedev Physical Institute of the Russian Academy of SciencesRU41 papers
7 papers · 1 filter
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…
The more legs the merrier: A new composition for symmetric (multi-)lenses
Michael Johnson, Robert Rosebrugh
Lenses are a category theoretic construct and are used in a wide variety of applications. Symmetric lenses compose to, of course, form new symmetric lenses. Symmetric lenses are us…
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…
Functional distribution monads in functional-analytic contexts
Rory B. B. Lucyshyn-Wright
We give a general categorical construction that yields several monads of measures and distributions as special cases, alongside several monads of filters. The construction takes pl…
A simplicial foundation for differential and sector forms in tangent categories
G. S. H. Cruttwell, Rory B. B. Lucyshyn-Wright
Tangent categories provide an axiomatic framework for understanding various tangent bundles and differential operations that occur in differential geometry, algebraic geometry, abs…
Cartesian differential categories revisited
G. S. H. Cruttwell
We revisit the definition of Cartesian differential categories, showing that a slightly more general version is useful for a number of reasons. As one application, we show that the…