Theorems · Theorem · category theory

CategoryTheory.Biprod.ofComponents_fst

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] {X₁ X₂ Y₁ Y₂ : C} (f₁₁ : X₁ ⟶ Y₁) (f₁₂ : X₁ ⟶ Y₂)
  (f₂₁ : X₂ ⟶ Y₁) (f₂₂ : X₂ ⟶ Y₂),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Biprod.ofComponents f₁₁ f₁₂ f₂₁ f₂₂)
      CategoryTheory.Limits.biprod.fst =
    CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.fst f₁₁ +
      CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.snd f₂₁

Defined in: Mathlib.CategoryTheory.Preadditive.Biproducts
Cited by: 0 results in Mathlib
Foundations: Depth 20 from the axioms · uses propext, Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasBinaryBiproducts

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites19

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
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Preadditivestatement and proof · cited by 3,309
add_zeroproof · cited by 2,707
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.Limits.comp_zeroproof · cited by 365
CategoryTheory.Limits.biprodstatement and proof · cited by 312
CategoryTheory.Limits.HasBinaryBiproductsstatement and proof · cited by 165
CategoryTheory.Limits.biprod.sndstatement and proof · cited by 132
CategoryTheory.Limits.biprod.inlproof · cited by 127

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.