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Tbilisi Mathematical Journal

Editor-in-Chief: Inassaridze, Hvedri

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Real sets

George Janelidze / Ross Street
Published Online: 2017-09-20 | DOI: https://doi.org/10.1515/tmj-2017-0101


After reviewing a universal characterization of the extended positive real numbers published by Denis Higgs in 1978, we define a category which provides an answer to the questions: what is a set with half an element? ∙ what is a set with π elements? The category of these extended positive real sets is equipped with a countable tensor product. We develop somewhat the theory of categories with countable tensors; we call the commutative such categories series monoidal and conclude by only briefly mentioning the non-commutative possibility called ω-monoidal. We include some remarks on sets having cardinalities in [-∞;∞].

MSC 2010: 18D10; 18D20; 20M14; 28A20

Keywords: Commutative monoid; biproduct; direct sum; abstract addition; magnitude module; series monoidal category


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About the article

Received: 2017-05-15

Accepted: 2017-09-07

Published Online: 2017-09-20

Published in Print: 2017-09-26

Citation Information: Tbilisi Mathematical Journal, Volume 10, Issue 3, Pages 23–49, ISSN (Online) 1512-0139, DOI: https://doi.org/10.1515/tmj-2017-0101.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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