Theorems · Theorem · category theory

CategoryTheory.ShortComplex.Splitting.leftHomologyData_K

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {S : CategoryTheory.ShortComplex C} [inst_2 : CategoryTheory.Limits.HasZeroObject C] (s : S.Splitting),
  s.leftHomologyData.K = S.X₁

Defined in: Mathlib.Algebra.Homology.ShortComplex.Exact
Cited by: 0 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasZeroObject

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.ShortComplex.X₁statement · cited by 889
CategoryTheory.ShortComplex.LeftHomologyData.Kstatement and proof · cited by 233
CategoryTheory.ShortComplex.Splittingstatement and proof · cited by 62
CategoryTheory.ShortComplex.Splitting.leftHomologyDatastatement and proof · cited by 5

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