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Mathlib/Algebra/Homology/ShortComplex
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lines changed Original file line number Diff line number Diff line change @@ -934,25 +934,13 @@ instance : F.PreservesMonomorphisms where
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exact ((S.map F).exact_iff_mono (by simp)).1
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(((S.exact_iff_mono rfl).2 hf).map F)
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- instance [Faithful F] [CategoryWithHomology C] : F.ReflectsMonomorphisms where
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- reflects {X Y} f hf := by
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- let S := ShortComplex.mk (0 : X ⟶ X) f zero_comp
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- exact (S.exact_iff_mono rfl).1
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- ((ShortComplex.exact_map_iff_of_faithful S F).1
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- (((S.map F).exact_iff_mono (by simp)).2 hf))
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instance : F.PreservesEpimorphisms where
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preserves {X Y} f hf := by
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let S := ShortComplex.mk f (0 : Y ⟶ Y) comp_zero
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exact ((S.map F).exact_iff_epi (by simp)).1
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(((S.exact_iff_epi rfl).2 hf).map F)
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- instance [Faithful F] [CategoryWithHomology C] : F.ReflectsEpimorphisms where
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- reflects {X Y} f hf := by
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- let S := ShortComplex.mk f (0 : Y ⟶ Y) comp_zero
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- exact (S.exact_iff_epi rfl).1
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- ((ShortComplex.exact_map_iff_of_faithful S F).1
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- (((S.map F).exact_iff_epi (by simp)).2 hf))
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end Functor
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