Theorems · Theorem · category theory

CategoryTheory.isIso_left_of_isIso_biprod_map

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] {W X Y Z : C} (f : W ⟶ Y) (g : X ⟶ Z)
  [CategoryTheory.IsIso (CategoryTheory.Limits.biprod.map f g)], CategoryTheory.IsIso f

If ``(f 0) (0 g)`is invertible, thenf` is invertible.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by: 1 results in Mathlib
Foundations: Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBinaryBiproducts CategoryTheory.IsIso

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Cites20

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.compproof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Category.id_compproof · cited by 1,998
CategoryTheory.IsIsostatement and proof · cited by 1,156
CategoryTheory.invproof · cited by 467
CategoryTheory.Limits.biprodstatement and proof · cited by 312
CategoryTheory.Limits.HasBinaryBiproductsstatement and proof · cited by 165
CategoryTheory.Limits.biprod.inlproof · cited by 127

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.isIso_right_of_isIso_biprod_mapproof · cited by 0