Theorems · Definition · group theory
CategoryTheory.Groupoid.vertexGroupIsomOfMap
{C : Type u} → [inst : CategoryTheory.Groupoid C] → {c d : C} → (c ⟶ d) → (c ⟶ c) ≃* (d ⟶ d)An arrow in the groupoid defines, by conjugation, an isomorphism of groups between its endpoints.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Groupoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- MulEquivstatement · cited by 1,142
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Groupoid.invproof · cited by 36
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Groupoid.vertexGroupIsomOfMap_applystatement and proof · cited by 0
- CategoryTheory.Groupoid.vertexGroupIsomOfMap_symm_applystatement and proof · cited by 0
- CategoryTheory.Groupoid.vertexGroupIsomOfPathproof · cited by 0