Suppose we have a small category $\mathcal{I}$, a diagram $D : \mathcal{I} \to \mathcal{C}$, and a functor $F : \mathcal{C} \to \mathcal{D}$. De know that the functor $\hat{F} : \text{Cone}_{\mathcal{C}}(D) \to \text{Cone}_\mathcal{D}(F \circ D)$ preserves the terminal object(s). In categories with zero objects (like Top), can we not use the $(—)^\text{op}$-functor for $F$ to show that the completeness of Top implies its cocompleteness..?
2026-03-20 05:00:21.1773982821
In categories with zero objects: completeness $\Leftrightarrow$ cocompleteness?
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