12 May 2009
2:30 - 4:00   Claudio Hermida
Monoidal Indeterminates

Given any symmetric monoidal category $\C$ and a sub-smc $\Sigma$, it is shown how to construct~$\C[\Sigma]$, a \emph{polynomial} such category, the result of freely adjoining to $\C$ a system of monoidal indeterminates for every object of $\Sigma$ satisfying a naturality constraint with the arrows of $\Sigma$. As a special case, we show how to construct the free coaffine category (symmetric monoidal category with initial unit) on a given small symmetric monoidal category. It is then shown that all the known categories of ``possible worlds'' used to treat languages that allow for dynamic creation of ``new'' variables, locations, or names are in fact instances of this construction and hence have appropriate universality properties.