Theorems · Definition · category theory

CategoryTheory.Limits.biprod.associator

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] → (P Q R : C) → (P ⊞ Q) ⊞ R ≅ P ⊞ Q ⊞ R

The associator isomorphism which associates a binary biproduct.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by: 6 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBinaryBiproducts

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Cites9

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
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.biprodstatement · cited by 312
CategoryTheory.Limits.HasBinaryBiproductsstatement and proof · cited by 165
CategoryTheory.Limits.biprod.sndproof · cited by 132
CategoryTheory.Limits.biprod.fstproof · cited by 121
CategoryTheory.Limits.biprod.liftproof · cited by 79

Cited by6

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.biprod.associator_homstatement and proof · cited by 1
CategoryTheory.Limits.biprod.associator_invstatement and proof · cited by 1
CategoryTheory.Limits.biprod.associator_inv_naturalstatement · cited by 1
CategoryTheory.Limits.biprod.associator_naturalstatement · cited by 1
CategoryTheory.Limits.biprod.associator_inv_natural_assocstatement and proof · cited by 0
CategoryTheory.Limits.biprod.associator_natural_assocstatement and proof · cited by 0