archives@tulane.edu / In this thesis, I define and study the foundations of the new framework of graded category theory, which I propose as just one structure that fits under the general banner of what Andree Eheresman has called “dynamic category theory”. Two approaches to defining graded categories are developed and shown to be equivalent formulations by a novel variation on the Grothendieck construction. Various notions of graded categorical constructions are studied within this framework. In particular, the structure of graded categories in general is then further elucidated by studying so-called “variable-object” models, and a version of the Yoneda lemma for graded categories. As graded category theory was originally developed in order to better understand the intuitive notions of absolute and relative cardinality – these notions are applied to the problem of vindicating the Skolemite thesis that “all sets, from an absolute perspective, are countable”. Finally, I discuss some open problems in this framework, discuss some potential applications, and discuss some of the relationships of my approach to existing approaches in the literature. / 1 / Nathan bedell