20/05/17 18:15:41 9UHEbX30.net
圏論の大家 William Lawvere 氏の古典的名著
集合論を圏論で書けるぞという話です。
（参考）
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Theory and Applications of Categories
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Reprints in Theory and Applications of Categories
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An elementary theory of the category of sets (long version) with commentary
F. William Lawvere 1964
緒言
The elementary theory presented in this paper is intended to accomplish two purposes.
First, the theory characterizes the category of sets and mappings as an abstract category in the sense that any model for the axioms which satisfies the additional (non-elementary) axiom of completeness (in the usual sense of category theory) can be proved to be equivalent to S.
Second, the theory provides a foundation for mathematics which is quite different from the usual set theories in the sense that much of number theory, elementary analysis, and algebra can apparently be developed within it even though no relation with the usual properties of ∈ can be defined.