Theorems · Theorem · category theory

CategoryTheory.Abelian.Ext.biprodAddEquiv_apply_fst

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.HasExt C] {X₁ X₂ Y : C} {n : ℕ} (e : CategoryTheory.Abelian.Ext (X₁ ⊞ X₂) Y n),
  (CategoryTheory.Abelian.Ext.biprodAddEquiv e).1 =
    (CategoryTheory.Abelian.Ext.mk₀ CategoryTheory.Limits.biprod.inl).comp e ⋯

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.HasExt

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Cites11

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

DFunLike.coestatement and proof · cited by 62,936
CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Abelianstatement and proof · cited by 1,753
AddEquivstatement · cited by 1,087
CategoryTheory.Limits.biprodstatement and proof · cited by 312
CategoryTheory.HasExtstatement and proof · cited by 218
CategoryTheory.Abelian.Extstatement and proof · cited by 191
CategoryTheory.Limits.biprod.inlstatement · cited by 127
CategoryTheory.Abelian.Ext.mk₀statement · cited by 94
CategoryTheory.Abelian.Ext.compstatement · cited by 80
CategoryTheory.Abelian.Ext.biprodAddEquivstatement and proof · cited by 5

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_applyproof · cited by 0