Theorems · Theorem · category theory

CategoryTheory.ShortComplex.mapHomologyIso.congr_simp

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] (S : CategoryTheory.ShortComplex C)
  (F : CategoryTheory.Functor C D) [inst_4 : F.PreservesZeroMorphisms] [inst_5 : S.HasHomology]
  [inst_6 : (S.map F).HasHomology] [inst_7 : F.PreservesLeftHomologyOf S], S.mapHomologyIso F = S.mapHomologyIso F

Defined in: Mathlib.Algebra.Homology.ShortComplex.PreservesHomology
Cited by: 0 results in Mathlib
Foundations: Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Functor.PreservesZeroMorphisms CategoryTheory.ShortComplex.HasHomology CategoryTheory.ShortComplex.HasHomology CategoryTheory.Functor.PreservesLeftHomologyOf

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
CategoryTheory.Functor.PreservesZeroMorphismsstatement and proof · cited by 458
CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
CategoryTheory.ShortComplex.homologystatement · cited by 216
CategoryTheory.ShortComplex.mapstatement and proof · cited by 188
CategoryTheory.Functor.PreservesLeftHomologyOfstatement and proof · cited by 35
CategoryTheory.ShortComplex.mapHomologyIsostatement and proof · cited by 12

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