Topology via enriched category theory

  • Derek Scott Cook

Student thesis: Doctoral Thesis


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 AwardSept 2021
Original languageEnglish
Awarding Institution
  • University of Portsmouth
SupervisorIttay Weiss (Supervisor) & Andrew Burbanks (Supervisor)

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