Theorems · Definition · category theory

CategoryTheory.Limits.biprod

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → (X Y : C) → [CategoryTheory.Limits.HasBinaryBiproduct X Y] → C

An arbitrary choice of biproduct of a pair of objects.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by: 312 results in Mathlib
Foundations: Depth 6 from the axioms, rests on 11 definitions · uses Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBinaryBiproduct

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Cites5

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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
CategoryTheory.Limits.BinaryBicone.ptproof · cited by 95
CategoryTheory.Limits.BinaryBiproduct.biconeproof · cited by 68

Cited by399

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.biprod.sndstatement · cited by 132
CategoryTheory.Limits.biprod.inlstatement · cited by 127
CategoryTheory.Limits.biprod.fststatement · cited by 121
CategoryTheory.Limits.biprod.inrstatement · cited by 109
CategoryTheory.Limits.biprod.liftstatement · cited by 79
HomologicalComplex.homotopyCofiber.Xproof · cited by 59
CategoryTheory.Limits.biprod.descstatement · cited by 54
CategoryTheory.Limits.biprod.hom_extstatement and proof · cited by 34
CategoryTheory.Limits.biprod.lift_sndstatement · cited by 33
CategoryTheory.Limits.biprod.lift_fststatement · cited by 31
CategoryTheory.Limits.biprod.hom_ext'statement and proof · cited by 30
CategoryTheory.Limits.biprod.mapstatement · cited by 27

Showing the 200 most cited of 399.