How complete is PER?

The category of partial equivalence relations (PER) on the natural numbers has been used extensively in recent years to model various forms of higher-order type theory. It is known that PER can be viewed as a category of sets in a nonstandard model of intuitionistic Zermelo-Fraenkel set theory. The use of PER as a vehicle for modeling-type theory then arises from completeness properties of this category. The paper demonstrates these completeness properties, and shows that, constructively, some complete categories are more complete than others.<
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