メモ https://ncatlab.org/nlab/show/ETCS ETCS Context Topos Theory Foundations Contents 1. Idea 2. Definition 3. A constructive view 4. A contemporary perspective 5. Todd Trimble’s exposition of ETCS (抜粋) 1. Idea The Elementary Theory of the Category of Sets , or ETCS for short, is an axiomatic formulation of set theory in a category-theoretic spirit. As such, it is the prototypical structural set theory. Proposed shortly after ETCC in (Lawvere 64) it is also the paradigm for a categorical foundation of mathematics.1
The theory intends to capture in an invariant way the notion of a (constant) ‘abstract set’ whose elements lack internal structure and whose on
