Axiomatizing a category of categories

Journal of Symbolic Logic 56 (4):1243-1260 (1991)
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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275472
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,169
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Abstractionist Categories of Categories.Shay Allen Logan - 2015 - Review of Symbolic Logic 8 (4):705-721.
Mathematical Structuralism Today.Julian C. Cole - 2010 - Philosophy Compass 5 (8):689-699.

View all 6 citations / Add more citations

Similar books and articles
Added to PP index
2009-01-28

Total downloads
50 ( #107,369 of 2,191,856 )

Recent downloads (6 months)
1 ( #288,547 of 2,191,856 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature