Theorems · Theorem · category theory

CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hg

∀ {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} (h : S.LeftHomologyData)
  (F : CategoryTheory.Functor C D) [inst_4 : F.PreservesZeroMorphisms] [h.IsPreservedBy F],
  CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.parallelPair S.g 0) F

When a left homology data is preserved by a functor F, this functor preserves the kernel of S.g : S.X₂ ⟶ S.X₃.

Defined in

Mathlib.Algebra.Homology.ShortComplex.PreservesHomology

Cited by

1 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy