Elementary theory of the category of sets
In mathematics, the elementary theory of the category of sets or ETCS is a set of axioms for set theory proposed by William Lawvere in 1964. Although it was originally stated in the language of category theory, as Tom Leinster pointed out, the axioms can be stated without references to category theory.
Source: Wikipedia — Elementary theory of the category of sets (CC BY-SA 4.0)