Investigations into the categorical foundations of homotopy theory - Hughes, Kenneth Robert (Department of Mathematics and Applied Mathematics, 2016)
The purpose of the thesis is twofold - to give an account of the categorical foundations of homotopy theory, and to illuminate some aspects of category theory by showing the role played by the formation or quotient categories in many parts of general theory. Chapter 1 defines and classifies various types of quotient functor and gives methods of construction. Chapter 2 gives examples of the behaviour of limits under quotient functors. Chapter 3 defines the concepts of a weakly representable functor and a (general) homotopy theory and characterizes them. Chapter 4 develops some theory on the structure of abelian categories in order to produce a pathological example of a homotopy theory. Chapter 5 embeds the quotient categories constructed from homotopy theories in complete categories.