Theorems · Theorem · category theory

CategoryTheory.ShortComplex.HomologyMapData.map_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] {S₁ S₂ : CategoryTheory.ShortComplex C} {φ : S₁ ⟶ S₂}
  {h₁ : S₁.HomologyData} {h₂ : S₂.HomologyData} (ψ : CategoryTheory.ShortComplex.HomologyMapData φ h₁ h₂)
  (F : CategoryTheory.Functor C D) [inst_4 : F.PreservesZeroMorphisms] [inst_5 : h₁.left.IsPreservedBy F]
  [inst_6 : h₁.right.IsPreservedBy F] [inst_7 : h₂.left.IsPreservedBy F] [inst_8 : h₂.right.IsPreservedBy F],
  (ψ.map F).right = ψ.right.map F

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.ShortComplex.LeftHomologyData.IsPreservedByCategoryTheory.ShortComplex.RightHomologyData.IsPreservedByCategoryTheory.ShortComplex.LeftHomologyData.IsPreservedByCategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy