Theorems · Theorem · category theory
CategoryTheory.FreeGroupoid.lift_spec
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {G : Type u₁} [inst_1 : CategoryTheory.Groupoid G]
(φ : CategoryTheory.Functor C G), (CategoryTheory.FreeGroupoid.of C).comp (CategoryTheory.FreeGroupoid.lift φ) = φ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 and proof · cited by 16,252
- CategoryTheory.Functor.compstatement · cited by 6,529
- CategoryTheory.Groupoidstatement and proof · cited by 182
- Prefunctor.compproof · cited by 35
- CategoryTheory.FreeGroupoidstatement · cited by 27
- CategoryTheory.Functor.toPrefunctorproof · cited by 24
- CategoryTheory.FreeGroupoid.ofstatement · cited by 21
- CategoryTheory.FreeGroupoid.liftstatement · cited by 12
- Quiver.FreeGroupoidproof · cited by 8
- Quiver.FreeGroupoid.ofproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.FreeGroupoid.functorEquivproof · cited by 2
- CategoryTheory.FreeGroupoid.lift_compproof · cited by 0
- CategoryTheory.FreeGroupoid.map_comp_liftproof · cited by 0
- CategoryTheory.FreeGroupoid.lift_id_comp_ofproof · cited by 0
- CategoryTheory.FreeGroupoid.lift_map_homMkproof · cited by 0
- CategoryTheory.FreeGroupoid.strictUniversalPropertyFixedTargetproof · cited by 0