Theorems · Theorem · category theory

CochainComplex.exactAt_op

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {K : CochainComplex C ℤ} {n : ℤ},
  HomologicalComplex.ExactAt K n →
    ∀ (m : ℤ),
      autoParam (n + m = 0) CochainComplex.exactAt_op._auto_1 →
        HomologicalComplex.ExactAt ((CochainComplex.opEquivalence C).functor.obj (Opposite.op K)) m

Defined in: Mathlib.Algebra.Homology.CochainComplexOpposite
Cited by: 1 results in Mathlib
Foundations: Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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Cites14

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
CategoryTheory.Functor.objstatement and proof · cited by 19,642
Oppositestatement · cited by 8,081
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.Equivalence.functorstatement and proof · cited by 1,268
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
HomologicalComplex.sc'proof · cited by 112
HomologicalComplex.ExactAtstatement and proof · cited by 44
CochainComplex.nextproof · cited by 13
HomologicalComplex.exactAt_iff'proof · cited by 10
CochainComplex.opEquivalencestatement and proof · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

CochainComplex.acyclic_opproof · cited by 1