Theorems · Theorem · category theory

CategoryTheory.Abelian.Ext.mapExactFunctor_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {D : Type u'}
  [inst_2 : CategoryTheory.Category.{v', u'} D] [inst_3 : CategoryTheory.Abelian D] (F : CategoryTheory.Functor C D)
  [inst_4 : F.Additive] [inst_5 : CategoryTheory.Limits.PreservesFiniteLimits F]
  [inst_6 : CategoryTheory.Limits.PreservesFiniteColimits F] [inst_7 : CategoryTheory.HasExt C]
  [inst_8 : CategoryTheory.HasExt D] {X Y Z : C} {a b : ℕ} (α : CategoryTheory.Abelian.Ext X Y a)
  (β : CategoryTheory.Abelian.Ext Y Z b) {c : ℕ} (h : a + b = c),
  CategoryTheory.Abelian.Ext.mapExactFunctor F (α.comp β h) =
    (CategoryTheory.Abelian.Ext.mapExactFunctor F α).comp (CategoryTheory.Abelian.Ext.mapExactFunctor F β) h

Defined in

Mathlib.Algebra.Homology.DerivedCategory.Ext.Map

Cited by

2 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Functor.AdditiveCategoryTheory.Limits.PreservesFiniteLimitsCategoryTheory.Limits.PreservesFiniteColimitsCategoryTheory.HasExtCategoryTheory.HasExt