Theorems · Definition · category theory

CategoryTheory.Functor.mapExtLinearMap

{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] →
                        (R : Type u_1) →
                          [inst_9 : Ring R] →
                            [inst_10 : CategoryTheory.Linear R C] →
                              [inst_11 : CategoryTheory.Linear R D] →
                                [CategoryTheory.Functor.Linear R F] →
                                  (X Y : C) →
                                    (n : ℕ) →
                                      CategoryTheory.Abelian.Ext X Y n →ₗ[R]
                                        CategoryTheory.Abelian.Ext (F.obj X) (F.obj Y) n

Upgrade of F.mapExtAddHom assuming F is linear.

Defined in

Mathlib.Algebra.Homology.DerivedCategory.Ext.Map

Cited by

3 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Functor.AdditiveCategoryTheory.Limits.PreservesFiniteLimitsCategoryTheory.Limits.PreservesFiniteColimitsCategoryTheory.HasExtCategoryTheory.HasExtRingCategoryTheory.LinearCategoryTheory.LinearCategoryTheory.Functor.Linear