Theorems · Inductive type · group theory
IsFreeGroupoid
(G : Type u_1) → [CategoryTheory.Groupoid G] → Type (max u_1 (v + 1))
A groupoid G is free when we have the following data:
- a quiver on IsFreeGroupoid.Generators G (a type synonym for G)
- a function of taking a generating arrow to a morphism in G
- such that a functor from G to any group X is uniquely determined
by assigning labels in X to the generating arrows.
This definition is nonstandard. Normally one would require that functors G ⥤ X
to any _groupoid_ X are given by graph homomorphisms from generators.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Groupoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Groupoidstatement · cited by 182
Cited by22
Results whose statement or proof uses this declaration.
- IsFreeGroupoid.ofstatement and proof · cited by 7
- IsFreeGroupoid.SpanningTree.homOfPathstatement and proof · cited by 4
- IsFreeGroupoid.SpanningTree.treeHomstatement and proof · cited by 4
- IsFreeGroupoid.SpanningTree.functorOfMonoidHomstatement and proof · cited by 3
- IsFreeGroupoid.SpanningTree.loopOfHomstatement and proof · cited by 3
- IsFreeGroupoid.ext_functorstatement and proof · cited by 2
- IsFreeGroupoid.unique_liftstatement and proof · cited by 2
- IsFreeGroupoid.SpanningTree.treeHom_eqstatement and proof · cited by 2
- IsFreeGroupoid.SpanningTree.loopOfHom_eq_idstatement and proof · cited by 1
- IsFreeGroupoid.SpanningTree.treeHom_rootstatement and proof · cited by 1
- IsFreeGroupoid.casesOnstatement and proof · cited by 0
- IsFreeGroupoid.ctorIdxstatement and proof · cited by 0