Theorems · Theorem · category theory

CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_H

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {S : CategoryTheory.ShortComplex C} (hS : S.Exact) [inst_2 : CategoryTheory.Limits.HasZeroObject C]
  (cc : CategoryTheory.Limits.CokernelCofork S.f) (hcc : CategoryTheory.Limits.IsColimit cc),
  (hS.rightHomologyDataOfIsColimitCokernelCofork cc hcc).H = 0

Defined in: Mathlib.Algebra.Homology.ShortComplex.Exact
Cited by: 0 results in Mathlib
Foundations: Depth 46 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
Quiver.Homstatement · cited by 32,603
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.X₂statement · cited by 1,115
CategoryTheory.ShortComplex.X₁statement · cited by 889
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
CategoryTheory.Limits.parallelPairstatement · cited by 766
CategoryTheory.ShortComplex.fstatement and proof · cited by 653
CategoryTheory.ShortComplex.Exactstatement and proof · cited by 292

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