Theorems · Theorem · category theory
CategoryTheory.FintypeCat.Action.isConnected_iff_transitive
∀ (G : Type u) [inst : Group G] (X : Action FintypeCat G) [Nonempty X.V.obj], CategoryTheory.PreGaloisCategory.IsConnected X ↔ MulAction.IsPretransitive G X.V.obj
A nonempty finite G-set is connected if and only if the G-action is transitive.
- Defined in
- Mathlib.CategoryTheory.Galois.Examples
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Finitestatement · cited by 3,029
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- FintypeCatstatement and proof · cited by 217
- Actionstatement and proof · cited by 206
- Action.Vstatement and proof · cited by 176
- MulAction.IsPretransitivestatement and proof · cited by 94
- CategoryTheory.PreGaloisCategory.IsConnectedstatement and proof · cited by 37
- CategoryTheory.FintypeCat.Action.isConnected_of_transitiveproof · cited by 1
- CategoryTheory.FintypeCat.Action.pretransitive_of_isConnectedproof · cited by 1
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