Theorems · Theorem · category theory

CategoryTheory.ShortComplex.i_cyclesMk

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type w}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC]
  [inst_3 : CategoryTheory.HasForget₂ C Ab] [inst_4 : CategoryTheory.Preadditive C]
  [inst_5 : (CategoryTheory.forget₂ C Ab).Additive] [inst_6 : (CategoryTheory.forget₂ C Ab).PreservesHomology]
  (S : CategoryTheory.ShortComplex C) [inst_7 : S.HasHomology] (x₂ : ↑((CategoryTheory.forget₂ C Ab).obj S.X₂))
  (hx₂ : (CategoryTheory.ConcreteCategory.hom ((CategoryTheory.forget₂ C Ab).map S.g)) x₂ = 0),
  (CategoryTheory.ConcreteCategory.hom ((CategoryTheory.forget₂ C Ab).map S.iCycles)) (S.cyclesMk x₂ hx₂) = x₂

Defined in

Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.HasForget₂CategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.Functor.PreservesHomologyCategoryTheory.ShortComplex.HasHomology