Theorems · Definition · group theory
CategoryTheory.Groupoid.vertexGroupIsomOfPath
{C : Type u} → [inst : CategoryTheory.Groupoid C] → {c d : C} → Quiver.Path c d → (c ⟶ c) ≃* (d ⟶ d)A path in the groupoid defines an isomorphism between its endpoints.
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- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Groupoid
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- MulEquivstatement · cited by 1,142
- CategoryTheory.Groupoidstatement and proof · cited by 182
- Quiver.Pathstatement and proof · cited by 166
- CategoryTheory.composePathproof · cited by 16
- CategoryTheory.Groupoid.vertexGroupIsomOfMapproof · cited by 2
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