Theorems · Theorem · category theory

CategoryTheory.Abelian.Ext.precomp.congr_simp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.HasExt C] {X Y : C} {n : ℕ} (α α_1 : CategoryTheory.Abelian.Ext X Y n),
  α = α_1 → ∀ (Z : C) {a b : ℕ} (h : n + a = b), α.precomp Z h = α_1.precomp Z h

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences
Cited by: 2 results in Mathlib
Foundations: Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.HasExt

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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
AddMonoidHomstatement · cited by 3,230
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.HasExtstatement and proof · cited by 218
CategoryTheory.Abelian.Extstatement and proof · cited by 191
CategoryTheory.Abelian.Ext.precompstatement and proof · cited by 15

Cited by2

Results whose statement or proof uses this declaration.

ModuleCat.projectiveDimension_quotSMulTop_eq_succ_of_isSMulRegularproof · cited by 1
CategoryTheory.Functor.mapExt_bijective_of_preservesProjectiveObjectsproof · cited by 0