Theorems · Theorem · category theory

CategoryTheory.NatTrans.leftDerived_id

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} D]
  [inst_2 : CategoryTheory.Abelian C] [inst_3 : CategoryTheory.HasProjectiveResolutions C]
  [inst_4 : CategoryTheory.Abelian D] (F : CategoryTheory.Functor C D) [inst_5 : F.Additive] (n : ℕ),
  CategoryTheory.NatTrans.leftDerived (CategoryTheory.CategoryStruct.id F) n =
    CategoryTheory.CategoryStruct.id (F.leftDerived n)

Defined in: Mathlib.CategoryTheory.Abelian.LeftDerived
Cited by: 0 results in Mathlib
Foundations: Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.HasProjectiveResolutions CategoryTheory.Abelian CategoryTheory.Functor.Additive

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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 · cited by 32,603
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.compproof · cited by 6,529
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
ComplexShape.downproof · cited by 605
CategoryTheory.HasProjectiveResolutionsstatement and proof · cited by 42
HomotopyCategory.homologyFunctorproof · cited by 36
CategoryTheory.Functor.leftDerivedstatement and proof · cited by 29
CategoryTheory.Functor.leftDerivedToHomotopyCategoryproof · cited by 12

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