lemma. preserves if creates [leinster2016basic, 5.3.6] [tt-0059]

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Let \(\mathscr {F}: {\cal C} \rightarrow {\cal D}\) be a functor and \({\cal J}\) a small category. Suppose that \({\cal D}\) has, and \(\mathscr {F}\) creates, limits of shape \({\cal J}\). Then \({\cal C}\) has, and \(\mathscr {F}\) preserves, limits of shape \({\cal J}\).