What is an example of a functor $$F : \mathsf{Set} \to \mathsf{Set}$$ which preserves finite coproducts, but not infinite coproducts? The functors preserving infinite coproducts are given by $T \times - : \mathsf{Set} \to \mathsf{Set}$ for some set $T$. If a functor preserves finite coproducts, ...