Theorems · Theorem · category theory

CategoryTheory.Biprod.inl_ofComponents

∀ {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.Limits.biprod.inl
      (CategoryTheory.Biprod.ofComponents f₁₁ f₁₂ f₂₁ f₂₂) =
    CategoryTheory.CategoryStruct.comp f₁₁ CategoryTheory.Limits.biprod.inl +
      CategoryTheory.CategoryStruct.comp f₁₂ CategoryTheory.Limits.biprod.inr

Defined in: Mathlib.CategoryTheory.Preadditive.Biproducts
Cited by: 1 results in Mathlib
Foundations: Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasBinaryBiproducts

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Cites17

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.Preadditivestatement and proof · cited by 3,309
add_zeroproof · cited by 2,707
CategoryTheory.Limits.zero_compproof · cited by 339
CategoryTheory.Limits.biprodstatement and proof · cited by 312
CategoryTheory.Limits.HasBinaryBiproductsstatement and proof · cited by 165
CategoryTheory.Limits.biprod.sndproof · cited by 132
CategoryTheory.Limits.biprod.inlstatement and proof · cited by 127
CategoryTheory.Limits.biprod.fstproof · cited by 121
CategoryTheory.Limits.biprod.inrstatement and proof · cited by 109

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Biprod.ofComponents_eqproof · cited by 0