Theorems · Theorem · category theory

CategoryTheory.ShortComplex.HomologyMapData.natTransApp_right

∀ {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 G : CategoryTheory.Functor C D} [inst_4 : F.PreservesZeroMorphisms] [inst_5 : G.PreservesZeroMorphisms]
  [inst_6 : F.PreservesLeftHomologyOf S] [inst_7 : G.PreservesLeftHomologyOf S] [inst_8 : F.PreservesRightHomologyOf S]
  [inst_9 : G.PreservesRightHomologyOf S] (h : S.HomologyData) (τ : F ⟶ G),
  (CategoryTheory.ShortComplex.HomologyMapData.natTransApp h τ).right =
    CategoryTheory.ShortComplex.RightHomologyMapData.natTransApp h.right τ

Defined in

Mathlib.Algebra.Homology.ShortComplex.PreservesHomology

Cited by

0 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesLeftHomologyOfCategoryTheory.Functor.PreservesLeftHomologyOfCategoryTheory.Functor.PreservesRightHomologyOfCategoryTheory.Functor.PreservesRightHomologyOf