Theorems · Theorem · category theory
CategoryTheory.PreGaloisCategory.card_aut_le_card_fiber_of_connected
∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] (F : CategoryTheory.Functor C FintypeCat)
[inst_1 : CategoryTheory.PreGaloisCategory C] [CategoryTheory.PreGaloisCategory.FiberFunctor F] (A : C)
[CategoryTheory.PreGaloisCategory.IsConnected A], Nat.card (CategoryTheory.Aut A) ≤ Nat.card (F.obj A).objIf A is connected, the cardinality of Aut A is smaller than the cardinality of the
fiber of A.
- Defined in
- Mathlib.CategoryTheory.Galois.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Finitestatement · cited by 3,029
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- Nat.cardstatement · cited by 844
- FintypeCatstatement and proof · cited by 217
- CategoryTheory.Autstatement and proof · cited by 96
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.