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Theorems · Theorem · category theory

CategoryTheory.Biprod.isIso_inl_iff_isZero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] (X Y : C),
  CategoryTheory.IsIso CategoryTheory.Limits.biprod.inl ↔ CategoryTheory.Limits.IsZero Y
Defined in
Mathlib.CategoryTheory.Simple
Cited by
1 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts
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Around this declaration

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CategoryTheory.indecomposable_of_simple · cited by 0CategoryTheory.indecompos…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.Limits.zero_comp · cited by 339Limits.zero_compCategoryTheory.Limits.biprod · cited by 312Limits.biprodCategoryTheory.Limits.IsZero · cited by 306Limits.IsZeroCategoryTheory.Limits.HasBinaryBiproducts · cited by 165Limits.HasBinaryBiproductsCategoryTheory.Limits.biprod.snd · cited by 132biprod.sndCategoryTheory.Limits.biprod.inl · cited by 127biprod.inlCategoryTheory.Limits.biprod.fst · cited by 121biprod.fstCategoryTheory.Limits.biprod.inr · cited by 109biprod.inrBiprod.isIso_inl_iff_isZeroCITED BYCITES

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Cited by1

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