Say, if $F: \mathcal{C} \to \mathcal{D}, G: \mathcal{C} \leftarrow \mathcal{D}$ give an equivalence of the categories $\mathcal{C}, \mathcal{D}$,F,G), could there also be $F',G'$, that don't give an equivalence of catgories?
2026-03-27 17:05:02.1774631102
Do functors between equivalent categories necessarily form equivalent categories
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The categories are either equivalent or not. This doesn’t mean all functors between them are equivalences. If two sets have the same cardinality, does that mean all functions between them are bijections?