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Axiomatizing a category of categories

Published online by Cambridge University Press:  12 March 2014

Colin McLarty
Colin McLarty*
Affiliation:
Department of Philosophy, Case Western Reserve University, Cleveland, Ohio 44106
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 4 , December 1991 , pp. 1243 - 1260
Copyright
Copyright © Association for Symbolic Logic 1991

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References

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