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Details of talk

TitleReal sets
PresenterRoss Howard Street (Macquarie University)
Author(s)Prof Ross Howard Street
SessionCategory Theory, Algebraic Topology, K-Theory
Time14:00:00 2017-12-12
Abstract


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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.