Theorems · Definition · category theory

CategoryTheory.FreeGroupoid.functorEquiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u_1} →
      [inst_1 : CategoryTheory.Groupoid D] →
        CategoryTheory.Functor (CategoryTheory.FreeGroupoid C) D ≃ CategoryTheory.Functor C D

Functors out of the free groupoid biject with functors out of the original category.

Defined in: Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory
Cited by: 2 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Groupoid

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

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.Functorstatement and proof · cited by 16,252
Equivstatement · cited by 8,337
CategoryTheory.Functor.compproof · cited by 6,529
CategoryTheory.Groupoidstatement and proof · cited by 182
CategoryTheory.FreeGroupoidstatement and proof · cited by 27
CategoryTheory.FreeGroupoid.ofproof · cited by 21
CategoryTheory.FreeGroupoid.liftproof · cited by 12
CategoryTheory.FreeGroupoid.lift_specproof · cited by 4

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Grpd.freeForgetAdjunctionproof · cited by 4
CategoryTheory.FreeGroupoid.functorEquiv_applystatement and proof · cited by 0
CategoryTheory.FreeGroupoid.functorEquiv_symm_applystatement and proof · cited by 0