Theorems · Definition · category theory
CategoryTheory.FreeGroupoid
(C : Type u) → [CategoryTheory.Category.{v, u} C] → Type uThe underlying type of the free groupoid on a category,
defined by quotienting the free groupoid on the underlying quiver of C
by the relation that promotes the prefunctor C ⥤q FreeGroupoid C into a functor
C ⥤ Quotient (FreeGroupoid.homRel C).
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- 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
- CategoryTheory.Quotientproof · cited by 48
- CategoryTheory.FreeGroupoid.homRelproof · cited by 3
Cited by40
Results whose statement or proof uses this declaration.
- CategoryTheory.FreeGroupoid.ofstatement · cited by 21
- CategoryTheory.FreeGroupoid.mapstatement · cited by 14
- CategoryTheory.FreeGroupoid.liftstatement · cited by 12
- CategoryTheory.FreeGroupoid.mkstatement · cited by 7
- CategoryTheory.Grpd.freeproof · cited by 6
- CategoryTheory.FreeGroupoid.lift_uniquestatement and proof · cited by 5
- CategoryTheory.FreeGroupoid.lift_specstatement · cited by 4
- CategoryTheory.FreeGroupoid.liftNatIso_hom_appstatement and proof · cited by 3
- CategoryTheory.FreeGroupoid.liftNatIso_inv_appstatement and proof · cited by 3
- CategoryTheory.FreeGroupoid.functorEquivstatement and proof · cited by 2
- CategoryTheory.FreeGroupoid.homMkstatement · cited by 2
- CategoryTheory.FreeGroupoid.liftNatIsostatement and proof · cited by 2