Category theory; homological algebra Categorical logic and toposes Concept
Elementary theory of the category of sets
Summary
The Elementary Theory of the Category of Sets (ETCS) is an axiomatic set theory proposed by Lawvere in 1964. It describes sets and functions through the way functions compose, instead of through a membership relation. Its models are the nondegenerate well-pointed toposes with a natural numbers object in which every epimorphism splits. It is weaker than Zermelo–Fraenkel set theory with choice, but strong enough for most ordinary mathematics.
Further reading
About this page
| Tag | W448SK1RTY |
|---|---|
| URI | m2://W448SK1RTY |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18B05, 03G30, 18A15 |
| Same as | |
| Changed | 2 November 2026 |
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