Theorems · Definition · category theory

CategoryTheory.Functor.mapExtAddHom

{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) →
              [F.Additive] →
                [CategoryTheory.Limits.PreservesFiniteLimits F] →
                  [CategoryTheory.Limits.PreservesFiniteColimits F] →
                    [inst_7 : CategoryTheory.HasExt C] →
                      [inst_8 : CategoryTheory.HasExt D] →
                        (X Y : C) →
                          (n : ℕ) → CategoryTheory.Abelian.Ext X Y n →+ CategoryTheory.Abelian.Ext (F.obj X) (F.obj Y) n

Upgraded of CategoryTheory.Abelian.Ext.mapExactFunctor into an additive homomorphism.

Defined in

Mathlib.Algebra.Homology.DerivedCategory.Ext.Map

Cited by

6 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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