Theorems · Definition · category theory
CategoryTheory.Groupoid.inv
{obj : Type u} → [self : CategoryTheory.Groupoid obj] → {X Y : obj} → (X ⟶ Y) → (Y ⟶ X)The inverse morphism
- Defined in
- Mathlib.CategoryTheory.Groupoid
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Groupoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Groupoidstatement and proof · cited by 182
Cited by50
Results whose statement or proof uses this declaration.
- CategoryTheory.Groupoid.inv_eq_invstatement · cited by 15
- CategoryTheory.Groupoid.invEquivalenceproof · cited by 8
- CategoryTheory.Core.functorToCoreproof · cited by 7
- CategoryTheory.Subgroupoid.IsNormal.conjstatement · cited by 6
- CategoryTheory.Subgroupoid.invstatement · cited by 6
- CategoryTheory.Groupoid.isoEquivHomproof · cited by 4
- CategoryTheory.Subgroupoid.mem_objs_of_srcproof · cited by 4
- CategoryTheory.Subgroupoid.extproof · cited by 3
- Quiver.FreeGroupoid.lift_uniqueproof · cited by 3
- CategoryTheory.Groupoid.vertexGroupIsomOfMapproof · cited by 2
- CategoryTheory.Subgroupoid.IsNormal.conj'statement and proof · cited by 2
- CategoryTheory.Subgroupoid.id_mem_of_nonempty_isotropyproof · cited by 2