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Theorems · Inductive type · category theory

CategoryTheory.PreGaloisCategory

(C : Type u₁) → [CategoryTheory.Category.{u₂, u₁} C] → Prop

Definition 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.

CategoryTheory.PreGaloisCategory.FiberFunctor · cited by 66PreGaloisCategory.FiberFu…CategoryTheory.PreGaloisCategory.evaluation_aut_injective_of_isConnected · cited by 6PreGaloisCategory.evaluat…CategoryTheory.PreGaloisCategory.evaluation_injective_of_isConnected · cited by 6PreGaloisCategory.evaluat…CategoryTheory.PreGaloisCategory.not_initial_of_inhabited · cited by 3PreGaloisCategory.not_ini…CategoryTheory.PreGaloisCategory.surjective_of_nonempty_fiber_of_isConnected · cited by 3PreGaloisCategory.surject…CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv · cited by 3PreGaloisCategory.fiberBi…CategoryTheory.PreGaloisCategory.fiberPullbackEquiv · cited by 3PreGaloisCategory.fiberPu…CategoryTheory.PreGaloisCategory.not_initial_iff_fiber_nonempty · cited by 2PreGaloisCategory.not_ini…CategoryTheory.PreGaloisCategory.fiberEqualizerEquiv · cited by 2PreGaloisCategory.fiberEq…CategoryTheory.PreGaloisCategory.initial_iff_fiber_empty · cited by 2PreGaloisCategory.initial…CategoryTheory.PreGaloisCategory.isIso_of_mono_of_eq_card_fiber · cited by 1PreGaloisCategory.isIso_o…CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epi · cited by 1PreGaloisCategory.surject…CategoryTheory.PreGaloisCategory.epi_of_nonempty_of_isConnected · cited by 1PreGaloisCategory.epi_of_…CategoryTheory.PreGaloisCategory.fiberPullbackEquiv_symm_fst_apply · cited by 1PreGaloisCategory.fiberPu…CategoryTheory.PreGaloisCategory.fiberPullbackEquiv_symm_snd_apply · cited by 1PreGaloisCategory.fiberPu…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.PreGaloisCateg…CITED BYCITES

Cites1

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Cited by31

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