Date of Award

Spring 2022

Document Type


Degree Name

Master of Arts (MA)



Committee Chairperson

Jeremy Brazas, Ph.D.

Committee Member

Michael Fisher, Ph.D.

Committee Member

Lin Tan, Ph.D.


We develop a functorial approach to quotient constructions, defining morphisms quotient relative to a functor and the dual concept of unique liftings relative to a functor. Various classes of epimorphism are given detailed analysis and their relationship to quotient morphisms characterized. The behavior of unique lifting morphisms with respect to products, equalizers, and general limits in a category are studied. Applications to generalized covering space theory, coreflective subcategories of topological spaces, topological groups and rings, and Galois theory are explored. Finally, we give conditions for the product of two quotient morphisms to be quotient in a braided monoidal closed category.