[Merged by Bors] - feat(CategoryTheory): Monotone.final_functor_iff#22101
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[Merged by Bors] - feat(CategoryTheory): Monotone.final_functor_iff#22101
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PR summary 887a6d2f29Import changes for modified filesNo significant changes to the import graph Import changes for all files
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Given a monotone map `f : J₁ → J₂` between preordered sets (with `J₁` directed), we show that the corresponding functor `J₁ ⥤ J₂` is final iff any element in `J₂` is smaller than or equal to an element in the image of `f`. (This is only a translation of a more general statement for filtered categories.)
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Given a monotone map
f : J₁ → J₂between preordered sets (withJ₁directed), we show that the corresponding functorJ₁ ⥤ J₂is final iff any element inJ₂is smaller than or equal to an element in the image off. (This is only a translation of a more general statement for filtered categories.)