Topology via enriched category theory

Abstract

In 1973, Lawvere observed that a metric space is nothing more than an enriched category. This has led to numerous and varied investigations that attempt to clarify and expand this link between metric analysis and category theory. This thesis addresses three fundamental concepts from analysis from an enriched categorical perspective: the topology induced by a metric, Lipschitz constants, and what might a “topology” induced by an enriched category in general be. A generalisation of Grothendieck fibrations is introduced to conveniently phrase an answer to the third question.

Date of Award	Sept 2021
Original language	English
Awarding Institution	University of Portsmouth
Supervisor	Ittay Weiss (Supervisor) & Andrew Burbanks (Supervisor)