maps is introduced to provide an instance of an algebraically compact category relative to a restricted class of functors. Algebraic compactness is a synthetic condition on a category which ensures solutions of recursive equations involving endofunctors of the category. We extend that result to include all internal functors on C when C is viewed as a full internal category of the effective topos. This is done using two general results: one about internal functors in general, and one about internal functors in the effective topos. The paper “Extensional PERs ” by P.Freyd, P.Mulry, G.Rosolini and D.Scott [2
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