Journal of Symbolic Logic

Axiomatizing a Category of Categories

Colin McLarty

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Abstract

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.

Article information

Source
J. Symbolic Logic, Volume 56, Issue 4 (1991), 1243-1260.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183743812

Mathematical Reviews number (MathSciNet)
MR1136454

Zentralblatt MATH identifier
0735.18001

JSTOR
links.jstor.org

Citation

McLarty, Colin. Axiomatizing a Category of Categories. J. Symbolic Logic 56 (1991), no. 4, 1243--1260. https://projecteuclid.org/euclid.jsl/1183743812


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