Theorems · Theorem · category theory

CategoryTheory.prod_id

∀ {C : Type u₁} [inst : CategoryTheory.CategoryStruct.{v₁, u₁} C] {D : Type u₂}
  [inst_1 : CategoryTheory.CategoryStruct.{v₂, u₂} D] (X : C) (Y : D),
  CategoryTheory.CategoryStruct.id (X, Y) =
    CategoryTheory.Prod.mkHom (CategoryTheory.CategoryStruct.id X) (CategoryTheory.CategoryStruct.id Y)

Defined in: Mathlib.CategoryTheory.Products.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 5 from the axioms · uses no axioms
Assumes: CategoryTheory.CategoryStruct CategoryTheory.CategoryStruct

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.idstatement · cited by 6,235
CategoryTheory.CategoryStructstatement and proof · cited by 343
CategoryTheory.Prod.mkHomstatement · cited by 108

Cited by2

Results whose statement or proof uses this declaration.

SSet.Truncated.HomotopyCategory.BinaryProduct.associativityIso_hom_appproof · cited by 1
CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_πproof · cited by 0