Theorems · Theorem · category theory

CategoryTheory.Biprod.column_nonzero_of_iso

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] {W X Y Z : C} (f : W ⊞ X ⟶ Y ⊞ Z) [CategoryTheory.IsIso f],
  CategoryTheory.CategoryStruct.id W = 0 ∨
    CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.inl
          (CategoryTheory.CategoryStruct.comp f CategoryTheory.Limits.biprod.fst) ≠
        0 ∨
      CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.inl
          (CategoryTheory.CategoryStruct.comp f CategoryTheory.Limits.biprod.snd) ≠
        0

Defined in

Mathlib.CategoryTheory.Preadditive.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproductsCategoryTheory.IsIso