Theorems · Theorem · category theory

CategoryTheory.ShortComplex.cyclesFunctor_obj

∀ (C : Type u_1) [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasKernels C] [inst_3 : CategoryTheory.Limits.HasCokernels C]
  (S : CategoryTheory.ShortComplex C), (CategoryTheory.ShortComplex.cyclesFunctor C).obj S = S.cycles

Defined in: Mathlib.Algebra.Homology.ShortComplex.LeftHomology
Cited by: 0 results in Mathlib
Foundations: Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasKernels CategoryTheory.Limits.HasCokernels

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
CategoryTheory.ShortComplex.cyclesstatement · cited by 220
CategoryTheory.Limits.HasKernelsstatement and proof · cited by 67
CategoryTheory.Limits.HasCokernelsstatement and proof · cited by 47
CategoryTheory.ShortComplex.cyclesFunctorstatement and proof · cited by 5

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