The MacLane problem on the set-theoretic foundation for category theory. II.
[For part I, see ibid. 102, 4018--4031 (2000; Zbl 0970.18001).] After giving a historical summary of the various ways that axiomatic set theory has failed to provide a satisfactory foundation for naive category theory (e.g., how does one account for the category of all categories), the authors proceed to the syntax and axiomatics of an extension of NBG (von Neumann-Bernays-Gödel set theory), called the two-sorted multi-rank theory of classes and sets. They then proceed to show how naive category theory may be formulated within this framework and finally ask the question of whether their system is a conservative extension of NBG.
scientific article; zbMATH DE number 1964709