Journal of Symbolic Logic 56 (4):1243-1260 (1991)
Elementary axioms describe a category of categories. Theorems of category theory follow, including some on adjunctions and triples. A new result is that associativity of composition in categories follows from cartesian closedness of the category of categories. The axioms plus an axiom of infinity are consistent iff the axioms for a well-pointed topos with separation axiom and natural numbers are. The theory is not finitely axiomatizable. Each axiom is independent of the others. Further independence and definability results are proved. Relations between categories and sets, the latter defined as discrete categories, are described, and applications to foundations are discussed
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Foundations of Unlimited Category Theory: What Remains to Be Done.Solomon Feferman - 2013 - Review of Symbolic Logic 6 (1):6-15.
The Prospects of Unlimited Category Theory: Doing What Remains to Be Done.Michael Ernst - 2015 - Review of Symbolic Logic 8 (2):306-327.
Abstractionist Categories of Categories.Shay Allen Logan - 2015 - Review of Symbolic Logic 8 (4):705-721.
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