Theorems · Definition · category theory
CategoryTheory.Cat.freeMapIdIso
(V : Type u_1) → [inst : Quiver V] → CategoryTheory.Cat.freeMap (𝟭q V) ≅ CategoryTheory.Functor.id (CategoryTheory.Paths V)
The functor free : Quiv ⥤ Cat preserves identities up to natural isomorphism and in fact up
to equality.
- Defined in
- Mathlib.CategoryTheory.Category.Quiv
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Quiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Iso.reflproof · cited by 727
- Quiverstatement and proof · cited by 405
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.Pathsstatement and proof · cited by 82
- Prefunctor.idstatement and proof · cited by 14
- CategoryTheory.Cat.freeMapstatement and proof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Cat.freeMap_idproof · cited by 0
- CategoryTheory.Cat.freeMapIdIso_hom_appstatement and proof · cited by 0
- CategoryTheory.Cat.freeMapIdIso_inv_appstatement and proof · cited by 0