Theorems · Definition · category theory
CategoryTheory.CategoryStruct.id
{obj : Type u} → [self : CategoryTheory.CategoryStruct.{v, u} obj] → (X : obj) → X ⟶ XThe identity morphism on an object.
- Defined in
- Mathlib.CategoryTheory.Category.Basic
- Cited by
- 6,235 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 5 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.CategoryStructstatement and proof · cited by 343
Cited by7,414
Results whose statement or proof uses this declaration.
- CategoryTheory.Category.comp_idstatement · cited by 2,119
- CategoryTheory.Category.id_compstatement · cited by 1,998
- CategoryTheory.Functor.constproof · cited by 1,264
- CategoryTheory.eqToHomproof · cited by 860
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Functor.map_idstatement · cited by 616
- CategoryTheory.Bicategory.leftUnitorstatement · cited by 309
- CategoryTheory.Iso.inv_hom_idstatement · cited by 308
- CategoryTheory.Bicategory.rightUnitorstatement · cited by 308
- CategoryTheory.Functor.associatorproof · cited by 276
- CategoryTheory.Iso.hom_inv_idstatement · cited by 264
- CategoryTheory.Pseudofunctor.mapIdstatement · cited by 175
Showing the 200 most cited of 7,414.