Theorems · Theorem · category theory

CategoryTheory.Functor.leftDerivedNatTrans.congr_simp

∀ {C : Type u_1} {D : Type u_2} {H : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_3, u_2} D] [inst_2 : CategoryTheory.Category.{v_5, u_3} H]
  (LF' LF : CategoryTheory.Functor D H) {F F' : CategoryTheory.Functor C H} {L : CategoryTheory.Functor C D}
  (α' α'_1 : L.comp LF' ⟶ F'),
  α' = α'_1 →
    ∀ (α α_1 : L.comp LF ⟶ F) (e_α : α = α_1) (W W_1 : CategoryTheory.MorphismProperty C) (e_W : W = W_1)
      [inst_3 : L.IsLocalization W] [inst_4 : LF.IsLeftDerivedFunctor α W] (τ τ_1 : F' ⟶ F),
      τ = τ_1 → LF'.leftDerivedNatTrans LF α' α W τ = LF'.leftDerivedNatTrans LF α'_1 α_1 W_1 τ_1

Defined in

Mathlib.CategoryTheory.Functor.Derived.LeftDerived

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Functor.IsLeftDerivedFunctor