Investigations into Contravariant Involutions

Abstract

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 Award	31 Dec 2022
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Renate Schmidt (Supervisor) & Andrea Schalk (Supervisor)