Theorems · Theorem · category theory

HomologicalComplex.Hom.inv_f_apply

∀ {ι : Type u_1} {V : Type u} [inst : CategoryTheory.Category.{v, u} V]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {c : ComplexShape ι} {C₁ C₂ : HomologicalComplex V c}
  (f : C₁ ⟶ C₂) [inst_2 : CategoryTheory.IsIso f] (j : ι), (CategoryTheory.inv f).f j = CategoryTheory.inv (f.f j)

Defined in: Mathlib.Algebra.Homology.HomologicalComplex
Cited by: 0 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.IsIso

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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.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
HomologicalComplex.Xstatement and proof · cited by 1,839
HomologicalComplexstatement and proof · cited by 1,691
ComplexShapestatement and proof · cited by 1,684
CategoryTheory.IsIsostatement and proof · cited by 1,156
HomologicalComplex.Hom.fstatement and proof · cited by 845
CategoryTheory.invstatement · cited by 467
CategoryTheory.IsIso.inv_hom_idproof · cited by 88
CategoryTheory.IsIso.eq_inv_of_inv_hom_idproof · cited by 10

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