Investigations into Contravariant Involutions

  • Toby Osborne

Student thesis: Phd


This thesis is about categories equipped with a contravariant involution. We study how to add such a structure using the product of a category with its opposite, we call this construction P. We show that we can equip P with a 2-comonad structure and that this lifts via a distributive law to the category of monoidal categories. We then show that in the specific setting of symmetric monoidal categories with strong monoidal functors P can also be equipped with a Frobenius pseudomonad structure. This means that in this setting it gives both the free and cofree way of adding an appropriate contravariant involution to a symmetric monoidal category. Finally we make some suggestions for extending this construction to traced and compact closed categories.
Date of Award31 Dec 2022
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorRenate Schmidt (Supervisor) & Andrea Schalk (Supervisor)


  • category theory
  • involutive categories
  • monoidal categories

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