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# Details of talk

Title Real sets Ross Howard Street (Macquarie University) Prof Ross Howard Street Category Theory, Algebraic Topology, K-Theory 14:00:00 2017-12-12 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: \begin{itemize} \item what is a set with half an element? \item what is a set with $\pi$ elements? \end{itemize} That is, we categorify (or objectify) the monoid $[0,\infty]$ under addition. 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 {\em series monoidal}. We may include some remarks on sets having cardinalities in $[-\infty,\infty]$. This is joint work with George Janelidze.