Theorems · Theorem · category theory

CategoryTheory.Functor.mapExtLinearMap_apply

∀ {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 : C) (n : ℕ) (R : Type u_1) [inst_9 : Ring R]
  [inst_10 : CategoryTheory.Linear R C] [inst_11 : CategoryTheory.Linear R D]
  [inst_12 : CategoryTheory.Functor.Linear R F] (e : CategoryTheory.Abelian.Ext X Y n),
  (F.mapExtLinearMap R X Y n) e = CategoryTheory.Abelian.Ext.mapExactFunctor F e

Defined in

Mathlib.Algebra.Homology.DerivedCategory.Ext.Map

Cited by

0 results in Mathlib

Foundations

Depth 117 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