Theorems · Definition · category theory

CategoryTheory.Limits.biprodIso

{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] → X ⨯ Y ≅ X ⨿ Y

The isomorphism between the specified binary product and the specified binary coproduct for a pair for a binary biproduct.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by: 0 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBinaryBiproduct

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Iso.transproof · cited by 566
CategoryTheory.Limits.pairproof · cited by 536
CategoryTheory.Limits.prodstatement · cited by 364
CategoryTheory.Limits.coprodstatement · cited by 252
CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
CategoryTheory.Limits.colimit.isColimitproof · cited by 193
CategoryTheory.Limits.limit.isLimitproof · cited by 146
CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIsoproof · cited by 67
CategoryTheory.Limits.IsLimit.conePointUniqueUpToIsoproof · cited by 57

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