Theorems · Theorem · category theory

CategoryTheory.PreGaloisCategory.FibreFunctor.end_isUnit

∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] [inst_1 : CategoryTheory.GaloisCategory C]
  (F : CategoryTheory.Functor C FintypeCat) [CategoryTheory.PreGaloisCategory.FiberFunctor F]
  (f : CategoryTheory.End F), IsUnit f

Any endomorphism of a fiber functor is a unit.

Defined in: Mathlib.CategoryTheory.Galois.Prorepresentability
Cited by: 0 results in Mathlib
Foundations: Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.GaloisCategory CategoryTheory.PreGaloisCategory.FiberFunctor

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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
IsUnitstatement · cited by 1,602
FintypeCatstatement and proof · cited by 217
CategoryTheory.Endstatement and proof · cited by 169
CategoryTheory.GaloisCategorystatement and proof · cited by 88
CategoryTheory.PreGaloisCategory.FiberFunctorstatement and proof · cited by 66
Group.isUnitproof · cited by 18
isUnit_map_iffproof · cited by 17
CategoryTheory.PreGaloisCategory.endMulEquivAutGaloisproof · cited by 3

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