Theorems · Definition · category theory
CategoryTheory.Abelian.Ext.biprodAddEquiv
{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} →
CategoryTheory.Abelian.Ext (X₁ ⊞ X₂) Y n ≃+
CategoryTheory.Abelian.Ext X₁ Y n × CategoryTheory.Abelian.Ext X₂ Y nExt commutes with binary biproducts on the first variable.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.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.sndproof · cited by 132
- CategoryTheory.Limits.biprod.inlproof · cited by 127
- CategoryTheory.Limits.biprod.fstproof · cited by 121
- CategoryTheory.Limits.biprod.inrproof · cited by 109
- CategoryTheory.Abelian.Ext.mk₀proof · cited by 94
- CategoryTheory.Abelian.Ext.compproof · cited by 80
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Ext.biprodAddEquiv_apply_fststatement and proof · cited by 1
- CategoryTheory.Abelian.Ext.biprodAddEquiv_apply_sndstatement and proof · cited by 1
- CategoryTheory.Abelian.Ext.biprodAddEquiv_symm_applystatement and proof · cited by 1
- CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sequenceIsoproof · cited by 1
- CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_applystatement and proof · cited by 0