Relative Weak Factorization Systems
Erin McCloskey

Abstract:
This thesis introduces and develops the notion of a relative weak factorization system. Motivated by research directions in type theory, we combine ideas from algebraic weak factorization systems with the concept of relative monads and comonads, to define a generalized, more flexible analogue of weak factorization systems, which is able to incorporate additional shapes of diagrams. We prove results regarding the properties of these systems and their relationships to existing notions of weak factorization systems.