Theorems · Theorem · category theory

CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.g

∀ {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} [self : h.IsPreservedBy F],
  CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.parallelPair S.g 0) F

the 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 19 from the axioms · uses propext

Assumes

CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy