Theorems · Theorem · category theory
CategoryTheory.FintypeCat.Action.isConnected_of_transitive
∀ (G : Type u) [inst : Group G] (X : FintypeCat) [inst_1 : MulAction G X.obj] [MulAction.IsPretransitive G X.obj] [h : Nonempty X.obj], CategoryTheory.PreGaloisCategory.IsConnected (Action.FintypeCat.ofMulAction G X)
A nonempty G-set with transitive G-action is connected.
- 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.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- Groupstatement and proof · cited by 6,238
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Finitestatement and proof · cited by 3,029
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- MulActionstatement and proof · cited by 1,294
- CategoryTheory.IsIsoproof · cited by 1,156
- CategoryTheory.Monoproof · cited by 893
- CategoryTheory.ObjectProperty.FullSubcategoryproof · cited by 726
- Nonempty.someproof · cited by 340
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.FintypeCat.Action.isConnected_iff_transitiveproof · cited by 0