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

Abstract
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.