Theorems · Theorem · category theory
CategoryTheory.ShortComplex.LeftHomologyData.mapLeftHomologyIso_eq
∀ {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} (hl : S.LeftHomologyData)
(F : CategoryTheory.Functor C D) [inst_4 : F.PreservesZeroMorphisms] [inst_5 : S.HasLeftHomology]
[inst_6 : F.PreservesLeftHomologyOf S],
S.mapLeftHomologyIso F = (hl.map F).leftHomologyIso ≪≫ F.mapIso hl.leftHomologyIso.symm- Cited by
- 0 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Iso.symmstatement and proof · cited by 993
- CategoryTheory.Functor.map_idproof · cited by 616
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