Theorems · Theorem · category theory

CategoryTheory.Abelian.Ext.hom_comp_singleFunctor_map_shift

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.HasExt C] [inst_3 : HasDerivedCategory C] {X Y Z : C} {n : ℕ}
  (x : CategoryTheory.Abelian.Ext X Y n) (f : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp x.hom
      ((CategoryTheory.shiftFunctor (DerivedCategory C) ↑n).map ((DerivedCategory.singleFunctor C 0).map f)) =
    (x.comp (CategoryTheory.Abelian.Ext.mk₀ f) ⋯).hom

Defined in

Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences

Cited by

3 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExtHasDerivedCategory