Multiversal Algebra

Abstract

This thesis discusses two ideas, multiversal algebra and algebraic enrichment, and one potential application for the latter, sequential scheduling. Multiversal algebra is a proposal for the reconsideration of semigroupoid and category theory within a framework that extends the approach of universal algebra. The idea is to introduce the notion of algebraic operation relative to a given binary relation, as an alternative to the notion of operation on a carrier class. It is shown that for a particular class of relations the derived notion of category coincides with that of standard category theory. Algebraic enrichment is the name given to a series of similar constructions translating between external and internal algebraic structure, which are studied as a first step towards generalizing the seminal results of Eckmann and Hilton, and for the application to sequential scheduling. This well-known combinatorial engine of game semantics is shown to form part of a double semigroupoid, and this new algebraic perspective on scheduling offers a new direction for the study of game models and their innocence condition.

Date of Award	16 Sept 2013
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Andrea Schalk (Main Supervisor)