The MacLane problem on set-theoretical foundations for the category theory
This paper, a translation from the original Russian [in: Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh. Temat. Obz. 63 (1999)], addresses the problem of devising set-theoretic axioms sufficient for treating naive category theory (including such questionable constructions as functor categories, etc.). The authors review and critique many of the approaches to solving MacLane's problem; and propose one of their own, based on a ``multi-rank theory of classes and sets''.
scientific article; zbMATH DE number 1551876