Theorems · Definition · category theory
CategoryTheory.PreGaloisCategory.autMulEquivAutGalois
{C : Type u₁} →
[inst : CategoryTheory.Category.{u₂, u₁} C] →
[inst_1 : CategoryTheory.GaloisCategory C] →
(F : CategoryTheory.Functor C FintypeCat) →
[CategoryTheory.PreGaloisCategory.FiberFunctor F] →
CategoryTheory.Aut F ≃* (CategoryTheory.PreGaloisCategory.AutGalois F)ᵐᵒᵖThe automorphism group of F is multiplicatively isomorphic to
(the multiplicative opposite of) the limit over the automorphism groups of
the Galois objects.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 119 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.Functorstatement and proof · cited by 16,252
- Finitestatement · cited by 3,029
- MulEquivstatement · cited by 1,142
- MulOppositestatement and proof · cited by 1,135
- MulEquiv.symmproof · cited by 482
- MonoidHom.compproof · cited by 469
- MonoidHomClass.toMonoidHomproof · cited by 294
- FintypeCatstatement and proof · cited by 217
- CategoryTheory.asIsoproof · cited by 177
- CategoryTheory.Autstatement and proof · cited by 96
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_appstatement and proof · cited by 1
- CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_πstatement · cited by 1
- CategoryTheory.PreGaloisCategory.autMulEquivAutGalois.congr_simpstatement and proof · cited by 0