Theorems · Theorem · category theory

CategoryTheory.Abelian.Ext.mapExactFunctor.congr_simp

∀ {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} (f f_1 : CategoryTheory.Abelian.Ext X Y n),
  f = f_1 → CategoryTheory.Abelian.Ext.mapExactFunctor F f = CategoryTheory.Abelian.Ext.mapExactFunctor F f_1

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Ext.Map
Cited by: 3 results in Mathlib
Foundations: Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.Functor.Additive CategoryTheory.Limits.PreservesFiniteLimits CategoryTheory.Limits.PreservesFiniteColimits CategoryTheory.HasExt CategoryTheory.HasExt

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
CategoryTheory.HasExtstatement and proof · cited by 218
CategoryTheory.Abelian.Extstatement and proof · cited by 191
CategoryTheory.Limits.PreservesFiniteLimitsstatement and proof · cited by 121
CategoryTheory.Limits.PreservesFiniteColimitsstatement and proof · cited by 102
CategoryTheory.Abelian.Ext.mapExactFunctorstatement and proof · cited by 15

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Abelian.Ext.mapExactFunctor₀proof · cited by 2
CategoryTheory.Functor.mapExt_bijective_of_preservesInjectiveObjectsproof · cited by 0
CategoryTheory.Functor.mapExt_bijective_of_preservesProjectiveObjectsproof · cited by 0