Theorems · Theorem · category theory

CochainComplex.HomComplex.Cochain.fromSingleMk.congr_simp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] {X : C} {K : CochainComplex C ℤ} {p q : ℤ} (f f_1 : X ⟶ K.X q),
  f = f_1 →
    ∀ {n : ℤ} (x : p + n = q) (T : CochainComplex.HomComplex.Triplet n),
      CochainComplex.HomComplex.Cochain.fromSingleMk f x T = CochainComplex.HomComplex.Cochain.fromSingleMk f_1 x T

Defined in: Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle
Cited by: 0 results in Mathlib
Foundations: Depth 68 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 and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Preadditivestatement and proof · cited by 3,309
HomologicalComplex.Xstatement and proof · cited by 1,839
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
CochainComplex.singleFunctorstatement · cited by 111
CochainComplex.HomComplex.Cochain.fromSingleMkstatement and proof · cited by 20
CochainComplex.HomComplex.Tripletstatement and proof · cited by 16
CochainComplex.HomComplex.Triplet.pstatement · cited by 12

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