838 名前：ly external property is cardinality with further external relations arising from mappings. The membership relation is local and relative i.e. membership is meaningful only between an element of a set and a subset of the very same set. (See Lawvere (1976, p.119) for a detailed description of the notion ‘abstract set’.2 3 4 5)
More in detail, ETCS is a first-order theory axiomatizing elementary toposes and specifically those which are well-pointed, have a natural numbers object and satisfy the axiom of choice. The theory omits the axiom of replacement, however.
2. Definition The axioms of ETCS can be summed up in one sentence as:
Definition 2.1. The category of sets is the topos which
