Thesis / Dissertation

Giving Daggers to Higher Cats: Generalised Quasi Operads, Astroidal Sets, and a Surface Operad

Michelle Louise Strumila, Marcy Robertson (ed.)

Published : 2020

Abstract

This thesis contains my work on various generalisations of infinity operads, as well as an example inspired by Topological Quantum Field Theories (TQFTs). The main result is a proof of the equivalence between the Segal and strict inner Kan conditions for graphical sets. There are two different generalisations of infinity operads explored herein. Firstly, there are dagger categories. Inspired by Hilbert spaces, the notion of adjoint is generalised to the category setting. Dagger categories assign to each morphism f : A -> B an adjoint f* : B -> A. One can then consider f to be a morphism between A and B rather than going in any particular direction A -> B or B -> A. A cyclic operad ..

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