Linear Functors and their Fixed Points

Abstract

In concurrent programming, message passing along channels plays a key role. This is a form of communication between two processes in which messages can be sent in both directions. To ensure the coherent sequencing of receiving and sending messages the communications on such a channel are goverened by a “protocol”. In this thesis, the categorical semantics of protocols for the message passing logic (introduced by Cockett and Pastro) is introduced. A special class of protocols, built on linear functors, is investigated and it is shown that these protocols naturally form linear functors.