A Coinductive Definition of Repletion

Abstract

Note. We work in an arbitrary topos E, where a subobject Σ of the subobject classifier Ω is given, which contains the truth value true. A subobject A ⊆ B is called a Σ-subobject if its classifying map factors through Σ; clearly, the factorization t : 1 → Σ of the generic subobject, classifies Σ-subobjects.