Theorems · Inductive type · category theory
CategoryTheory.PreGaloisCategory
(C : Type u₁) → [CategoryTheory.Category.{u₂, u₁} C] → PropDefinition of a (Pre)Galois category. Lenstra, Def 3.1, (G1)-(G3)
- Defined in
- Mathlib.CategoryTheory.Galois.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by31
Results whose statement or proof uses this declaration.
- CategoryTheory.PreGaloisCategory.FiberFunctorstatement · cited by 66
- CategoryTheory.PreGaloisCategory.evaluation_aut_injective_of_isConnectedstatement and proof · cited by 6
- CategoryTheory.PreGaloisCategory.evaluation_injective_of_isConnectedstatement and proof · cited by 6
- CategoryTheory.PreGaloisCategory.not_initial_of_inhabitedstatement and proof · cited by 3
- CategoryTheory.PreGaloisCategory.surjective_of_nonempty_fiber_of_isConnectedstatement and proof · cited by 3
- CategoryTheory.PreGaloisCategory.fiberBinaryProductEquivstatement and proof · cited by 3
- CategoryTheory.PreGaloisCategory.fiberPullbackEquivstatement and proof · cited by 3
- CategoryTheory.PreGaloisCategory.not_initial_iff_fiber_nonemptystatement and proof · cited by 2
- CategoryTheory.PreGaloisCategory.fiberEqualizerEquivstatement and proof · cited by 2
- CategoryTheory.PreGaloisCategory.initial_iff_fiber_emptystatement and proof · cited by 2
- CategoryTheory.PreGaloisCategory.isIso_of_mono_of_eq_card_fiberstatement and proof · cited by 1
- CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epistatement and proof · cited by 1