Theorems · Theorem · category theory

CategoryTheory.Functor.mapExt_bijective_of_preservesInjectiveObjects

∀ {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] [F.Full] [F.Faithful] [inst_9 : CategoryTheory.HasExt C]
  [inst_10 : CategoryTheory.HasExt D] [CategoryTheory.EnoughInjectives C] [F.PreservesInjectiveObjects] (X Y : C)
  (n : ℕ), Function.Bijective ⇑(F.mapExtAddHom X Y n)

Defined in

Mathlib.Algebra.Homology.DerivedCategory.Ext.MapBijective

Cited by

0 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Functor.AdditiveCategoryTheory.Limits.PreservesFiniteLimitsCategoryTheory.Limits.PreservesFiniteColimitsCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulCategoryTheory.HasExtCategoryTheory.HasExtCategoryTheory.EnoughInjectivesCategoryTheory.Functor.PreservesInjectiveObjects