Theorems · Theorem · category theory

CategoryTheory.ShortComplex.HasRightHomology.hasKernel

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (S : CategoryTheory.ShortComplex C) [S.HasRightHomology] [inst_3 : CategoryTheory.Limits.HasCokernel S.f],
  CategoryTheory.Limits.HasKernel (CategoryTheory.Limits.cokernel.desc S.f S.g ⋯)

Defined in: Mathlib.Algebra.Homology.ShortComplex.RightHomology
Cited by: 1 results in Mathlib
Foundations: Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.ShortComplex.HasRightHomology CategoryTheory.Limits.HasCokernel

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Cites40

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.objproof · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Isoproof · 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.ShortComplex.X₂statement · cited by 1,115
CategoryTheory.Iso.symmproof · cited by 993
CategoryTheory.ShortComplex.X₁statement · cited by 889
CategoryTheory.ShortComplex.X₃statement · cited by 876
CategoryTheory.Limits.parallelPairproof · cited by 766

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.ShortComplex.exact_iff_kernel_ι_comp_cokernel_π_zeroproof · cited by 3