A Fibrational Theory of First Order Differential Structures
Category Theory
2024-09-10 v1 Logic in Computer Science
Abstract
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of several existing categorical structures for differentiation, including cartesian differential categories, generalised cartesian differential categories, tangent categories, as well as the versions of these categories axiomatising reverse derivatives. We explain uniformly and concisely the requirements expressed by these structures, using sections of suitable fibrations as unifying concept. Our perspective sheds light on their similarities and differences, as well as simplifying certain constructions from the literature.
Keywords
Cite
@article{arxiv.2409.05763,
title = {A Fibrational Theory of First Order Differential Structures},
author = {Matteo Capucci and Geoffrey S. H. Cruttwell and Neil Ghani and Fabio Zanasi},
journal= {arXiv preprint arXiv:2409.05763},
year = {2024}
}