Supposing we have a model of the Elementary Theory of the Category of Sets (nLab article) which has all colimits. Is every set isomorphic to a coproduct of terminal objects (indexed over some discrete category)?
2026-03-29 07:00:31.1774767631
In a model of ETCS with all colimits, is every set isomorphic to a coproduct of 1's?
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As Lawvere proves in his original paper, any models of ETCS with small products and coproducts are equivalent. Thus such a category as you request is equivalent to the usual category of sets.