Title: Actegories and Copowers with Application to Message Passing Semantics
Abstract: In this talk we prove that giving a right actegory with hom-objects is equivalent to giving a right-enriched category with copowers. While this result is known in the closed symmetric setting, our contribution extends the equivalence to non-closed and non-symmetric monoidal bases. This generalization is motivated by the semantics of higher-order message passing in the \textbf{Categorical Message Passing Language (CaMPL)}, a concurrent language whose semantics is given by a linear actegory. A desirable feature for this language is the support of higher-order processes: processes that are passed as first class citizens between processes. While this ability is already present in any closed linear type systems — such as {\bf CaMPL}’s — to support arbitrary recursive process definitions requires the ability to reuse passed processes. Concurrent resources in {\bf CaMPL}, however, cannot be duplicated, thus, passing processes as linear closures does not provide the required flexibility. This means processes must be passed as sequential data and the concurrent side must be {\em enriched} in the sequential side, motivating the technical result of this paper.
