Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.lift_snd_assoc

∀ {C : Type uC} [inst : CategoryTheory.Category.{uC', uC} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {W X Y : C} [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X Y] (f : W ⟶ X) (g : W ⟶ Y) {Z : C} (h : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.lift f g)
      (CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.snd h) =
    CategoryTheory.CategoryStruct.comp g h

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by: 4 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBinaryBiproduct

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Cites10

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.compstatement and proof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.biprodstatement · cited by 312
CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
CategoryTheory.Limits.biprod.sndstatement and proof · cited by 132
CategoryTheory.Limits.biprod.liftstatement and proof · cited by 79
CategoryTheory.Limits.biprod.lift_sndproof · cited by 33

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.biprod.associator_inv_naturalproof · cited by 1
CategoryTheory.Limits.biprod.associator_naturalproof · cited by 1
CategoryTheory.Limits.biprod.braid_naturalproof · cited by 1
CategoryTheory.Limits.biprod.braiding_map_braidingproof · cited by 1