 Terminal finite-coproduct-preserving set endofunctor

ID: terminal-finite-coproduct-preserving-set-endofunctor

The ultrafilter functor is terminal among endofunctors of

Set

that preserve finite coproducts. For such an endofunctor

F

and

x \in F (A)

, the unique natural map sends

x

{B \subseteq A : x \in im (F (B) \to F (A))} .

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