Categorical magnitude and entropy
Category Theory
2023-12-14 v2 Information Theory
math.IT
Abstract
Given any finite set equipped with a probability measure, one may compute its Shannon entropy or information content. The entropy becomes the logarithm of the cardinality of the set when the uniform probability is used. Leinster introduced a notion of Euler characteristic for certain finite categories, also known as magnitude, that can be seen as a categorical generalization of cardinality. This paper aims to connect the two ideas by considering the extension of Shannon entropy to finite categories endowed with probability, in such a way that the magnitude is recovered when a certain choice of "uniform" probability is made.
Keywords
Cite
@article{arxiv.2303.00879,
title = {Categorical magnitude and entropy},
author = {Stephanie Chen and Juan Pablo Vigneaux},
journal= {arXiv preprint arXiv:2303.00879},
year = {2023}
}
Comments
11 pages, published in GSI 2023 conference proceedings