Future, large-scale, exoplanet direct-imaging missions will be capable of discovering and characterizing Earth-like exoplanets. These mission designs can evaluated using completeness, the fraction planets from some population that are detectable by a telescope at an arbitrary observation time. However, original formulation completeness uses instrument visibility limits ignores additional integr...

‎In this paper‎, ‎we prove that the category of crossed polymodules (i.e‎. ‎crossed modules of polygroups) and their morphisms is finitely complete‎. ‎We‎, ‎therefore‎, ‎generalize the group theoretical case of this completeness property of crossed modules‎.