Categorical magnitude and entropy
| Autor: | Chen, Stephanie, Vigneaux, Juan Pablo |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/978-3-031-38271-0_28 |
| Popis: | 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. Comment: 11 pages, published in GSI 2023 conference proceedings |
| Databáze: | arXiv |
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