Theorems · Theorem · category theory
CategoryTheory.PreGaloisCategory.lt_card_fiber_of_mono_of_notIso
∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] (F : CategoryTheory.Functor C FintypeCat)
[inst_1 : CategoryTheory.PreGaloisCategory C] [CategoryTheory.PreGaloisCategory.FiberFunctor F] {X Y : C} (f : X ⟶ Y)
[CategoryTheory.Mono f], ¬CategoryTheory.IsIso f → Nat.card (F.obj X).obj < Nat.card (F.obj Y).objAlong a mono that is not an iso, the cardinality of the fiber strictly increases.
- Defined in
- Mathlib.CategoryTheory.Galois.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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
- Quiver.Homstatement and proof · cited by 32,603
- 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.ConcreteCategory.homproof · cited by 4,022
- Finitestatement · cited by 3,029
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- Nat.cardstatement and proof · cited by 844
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