[Merged by Bors] - feat(category_theory/limits): preservation of zero morphisms #12068
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TwoFX
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| F.map (0 : X ⟶ Y) = 0 := | ||
| preserves_zero_morphisms.map_zero' _ _ | ||
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| lemma equivalence_preserves_zero_morphisms (F : C ≌ D) : preserves_zero_morphisms F.functor := |
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Is this a special case of something slightly more general, maybe that adjoints preserve zero morphisms? I don't know the maths here enough to be sure
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Earlier today I proved on paper that fully faithful is enough, and I'll generalize the proof soon. lt might also be true for adjoints, I'll think about that.
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I managed to prove it for adjoints :) I'll update the PR tomorrow. (Edit: Done.)
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| We provide the following results: | ||
| * Left adjoints and right adjoints preserve zero morphisms; | ||
| * full functors preserves zero morphisms; |
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| * full functors preserves zero morphisms; | |
| * full functors preserve zero morphisms; |
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