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arXiv · 2303.00879

Categorical magnitude and entropy

Stephanie Chen·Juan Pablo Vigneaux
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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.

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Stephanie Chen, Juan Pablo Vigneaux. 2023-03-02. Categorical magnitude and entropy. https://doi.org/10.1007/978-3-031-38271-0_28

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