Theorems · Theorem · category theory

CochainComplex.HomComplex.Cocycle.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)
  (e_f : f = f_1) {n : ℤ} (h : p + n = q) (q' q'_1 : ℤ) (e_q' : q' = q'_1) (hq' : q + 1 = q')
  (hf : CategoryTheory.CategoryStruct.comp f (K.d q q') = 0),
  CochainComplex.HomComplex.Cocycle.fromSingleMk f h q' hq' hf =
    CochainComplex.HomComplex.Cocycle.fromSingleMk f_1 h q'_1 ⋯ ⋯

Defined in: Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle
Cited by: 7 results in Mathlib
Foundations: Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasZeroObject

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Cites13

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 and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
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
HomologicalComplex.dstatement and proof · cited by 598
CochainComplex.HomComplex.Cocyclestatement · cited by 130
CochainComplex.singleFunctorstatement · cited by 111

Cited by7

Results whose statement or proof uses this declaration.

CategoryTheory.InjectiveResolution.extMk_surjectiveproof · cited by 0
CategoryTheory.InjectiveResolution.extMk_zeroproof · cited by 0
CategoryTheory.InjectiveResolution.neg_extMkproof · cited by 0
CategoryTheory.InjectiveResolution.mk₀_comp_extMkproof · cited by 0
CategoryTheory.InjectiveResolution.sub_extMkproof · cited by 0
CategoryTheory.InjectiveResolution.add_extMkproof · cited by 0
CategoryTheory.InjectiveResolution.extMk_comp_mk₀proof · cited by 0