Theorems · Theorem · category theory
CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected
∀ (G : Type u) [inst : Group G] (X : Action FintypeCat G) [CategoryTheory.PreGaloisCategory.IsConnected X], MulAction.IsPretransitive G X.V.obj
The G-action on a connected finite G-set is transitive.
- Defined in
- Mathlib.CategoryTheory.Galois.Examples
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Quiver.Homproof · cited by 32,603
- Fintypeproof · cited by 7,736
- Set.Elemproof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Finitestatement · cited by 3,029
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- MulActionproof · cited by 1,294
- CategoryTheory.IsIsoproof · cited by 1,156
- CategoryTheory.Monoproof · cited by 893
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.FintypeCat.Action.isConnected_iff_transitiveproof · cited by 0