Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.Bicategory.Strict.comp_id

∀ {B : Type u} {inst : CategoryTheory.Bicategory B} [self : CategoryTheory.Bicategory.Strict B] {a b : B} (f : a ⟶ b),
  CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.id b) = f

Identity morphisms are right identities for composition.

Defined in
Mathlib.CategoryTheory.Bicategory.Strict.Basic
Cited by
4 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CategoryTheory.Bicategory.Strict
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Bicategory.Strict.rightUnitor_eqToIso · cited by 5Strict.rightUnitor_eqToIsoCategoryTheory.Pseudofunctor.mapComp'_comp_id · cited by 4Pseudofunctor.mapComp'_co…CategoryTheory.Pseudofunctor.Grothendieck.map_id_eq · cited by 0Grothendieck.map_id_eqCategoryTheory.Pseudofunctor.CoGrothendieck.map_id_eq · cited by 0CoGrothendieck.map_id_eqQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Bicategory · cited by 1587CategoryTheory.BicategoryCategoryTheory.Bicategory.Strict · cited by 87Bicategory.StrictStrict.comp_idCITED BYCITES

Cites5

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

Cited by4

Results whose statement or proof uses this declaration.