Date of Award
Spring 2022
Document Type
Thesis
Degree Name
Master of Arts (MA)
Department
Mathematics
Committee Chairperson
Jeremy Brazas, Ph.D.
Committee Member
Michael Fisher, Ph.D.
Committee Member
Lin Tan, Ph.D.
Abstract
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.
Recommended Citation
Myers, Mark, "Unique Lifting to a Functor" (2022). West Chester University Master’s Theses. 237.
https://digitalcommons.wcupa.edu/all_theses/237