Theorems · Theorem · category theory

CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (S : CategoryTheory.ShortComplex C) [inst_2 : S.HasLeftHomology] {kf : CategoryTheory.Limits.KernelFork S.g}
  (hkf : CategoryTheory.Limits.IsLimit kf),
  CategoryTheory.CategoryStruct.comp (S.isoCyclesOfIsLimit hkf).hom S.iCycles = CategoryTheory.Limits.Fork.ι kf

Defined in: Mathlib.Algebra.Homology.ShortComplex.LeftHomology
Cited by: 1 results in Mathlib
Foundations: Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.ShortComplex.HasLeftHomology

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Cites21

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
Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Iso.homstatement · cited by 7,684
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
CategoryTheory.ShortComplex.X₂statement · cited by 1,115
CategoryTheory.ShortComplex.X₃statement · cited by 876
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.parallelPairstatement · cited by 766
CategoryTheory.Limits.IsLimitstatement and proof · cited by 664

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles_assocproof · cited by 2