Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.isoProd_hom

∀ {C : Type uC} [inst : CategoryTheory.Category.{uC', uC} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {X Y : C} [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X Y],
  (CategoryTheory.Limits.biprod.isoProd X Y).hom =
    CategoryTheory.Limits.prod.lift CategoryTheory.Limits.biprod.fst CategoryTheory.Limits.biprod.snd

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by: 3 results in Mathlib
Foundations: Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBinaryBiproduct

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Cites28

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 · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Iso.homstatement and proof · cited by 7,684
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.prodstatement · cited by 364
CategoryTheory.Limits.biprodstatement · cited by 312
CategoryTheory.Limits.limit.lift_πproof · cited by 266
CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
CategoryTheory.Limits.prod.fstproof · cited by 189
CategoryTheory.Limits.prod.sndproof · cited by 185

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.biprod.isoProd_invproof · cited by 2
CategoryTheory.Limits.preservesBinaryBiproduct_of_mono_biprodComparisonproof · cited by 1
CategoryTheory.Pretriangulated.binaryProductTriangleIsoBinaryBiproductTriangle_inv_hom₂proof · cited by 0