Categorial L\'evy Processes
Malte Gerhold, Stephanie Lachs, Michael Schürmann · arXiv (Cornell University) · 2016
We generalize Franz independence in tensor categories with inclusions from two morphisms (which represent generalized random variables) to arbitrary ordered families of morphisms. We will see that this only works consistently if the unit object is an initial object, in which case the inclusions can be defined starting from the tensor category alone. We define categorial L\'evy processes on every tensor categoriy with initial unit object and present a construction generalizing the reconstruction of a L\'evy process from its convolution semigroup via the Daniell-Kolmogorov theorem.