More exact completions that are toposes Original Research Article

Assuming some extra structure (present in realizability and localic examples) we simplify the characterization of the categories with finite limits whose exact completions are toposes given in Menni (J. Pure Appl. Algebra, to appear). This simplification allows us to obtain new examples and non-examples and also to provide a new perspective and an alternative proof of recent results on the inevitability of untypedness for realizability toposes.