Abstract
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 [-∞,∞].
| Original language | English |
|---|---|
| Pages (from-to) | 23-49 |
| Number of pages | 27 |
| Journal | Tbilisi mathematical journal |
| Volume | 10 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2017 |
Bibliographical note
Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.Keywords
- Commutative monoid
- biproduct
- direct sum
- abstract addition
- magnitude module
- series monoidal category