Theorems · Theorem · category theory

CategoryTheory.Limits.coprod.map_codiag

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y)
  [inst_1 : CategoryTheory.Limits.HasBinaryCoproduct X X] [inst_2 : CategoryTheory.Limits.HasBinaryCoproduct Y Y],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.coprod.map f f) (CategoryTheory.Limits.codiag Y) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.codiag X) f

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
Cited by: 1 results in Mathlib
Foundations: Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasBinaryCoproduct CategoryTheory.Limits.HasBinaryCoproduct

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites13

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 · cited by 17,999
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.Category.id_compproof · cited by 1,998
CategoryTheory.Limits.coprodstatement · cited by 252
CategoryTheory.Limits.HasBinaryCoproductstatement and proof · cited by 81
CategoryTheory.Limits.coprod.descproof · cited by 69
CategoryTheory.Limits.coprod.mapstatement · cited by 49
CategoryTheory.Limits.coprod.desc_compproof · cited by 22
CategoryTheory.Limits.coprod.map_descproof · cited by 16

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.coprod.map_codiag_assocproof · cited by 0