Limits and Colimits in a Category of Lenses
Category Theory
2022-11-04 v2
Abstract
Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we study the category of small categories and asymmetric delta lenses, and prove that it has several good exactness properties. These properties include the existence of certain limits and colimits, as well as so-called imported limits, such as imported products and imported pullbacks, which have arisen previously in applications. The category is also shown to be extensive, and it has an image factorisation system.
Keywords
Cite
@article{arxiv.2105.05422,
title = {Limits and Colimits in a Category of Lenses},
author = {Emma Chollet and Bryce Clarke and Michael Johnson and Maurine Songa and Vincent Wang and Gioele Zardini},
journal= {arXiv preprint arXiv:2105.05422},
year = {2022}
}
Comments
In Proceedings ACT 2021, arXiv:2211.01102