Theorems · Definition · category theory
CategoryTheory.Functor.id
(C : Type u₁) → [inst : CategoryTheory.Category.{v₁, u₁} C] → CategoryTheory.Functor C C𝟭 C is the identity functor on a category C.
- Defined in
- Mathlib.CategoryTheory.Functor.Basic
- Cited by
- 3,333 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 42 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
Cited by4,190
Results whose statement or proof uses this declaration.
- CategoryTheory.Overproof · cited by 935
- CategoryTheory.Arrowproof · cited by 713
- CategoryTheory.Equivalence.unitIsostatement · cited by 536
- CategoryTheory.Equivalence.counitIsostatement · cited by 480
- CategoryTheory.Adjunction.unitstatement · cited by 387
- CategoryTheory.Adjunction.counitstatement · cited by 376
- CategoryTheory.Underproof · cited by 276
- CategoryTheory.Over.forgetproof · cited by 164
- CategoryTheory.Functor.rightUnitorstatement · cited by 149
- CategoryTheory.Functor.leftUnitorstatement · cited by 117
- CategoryTheory.SimplicialObject.Augmentedproof · cited by 113
- CategoryTheory.Over.mapproof · cited by 97
Showing the 200 most cited of 4,190.