@@ -107,7 +107,7 @@ def FiniteEtale.baseChange : FiniteEtale.{v} R ⥤ FiniteEtale.{max w v} S where
107107 map {A B} f := FiniteEtale.ofHom (Algebra.TensorProduct.map (.id _ _) f.hom.hom)
108108
109109/-- Base change from `R` to `R` is isomorphic to the identity. -/
110- @ [expose, simps! ]
110+ @[expose]
111111def FiniteEtale.baseChangeSelfIso : baseChange R R ≅ 𝟭 (FiniteEtale R) :=
112112 NatIso.ofComponents (fun A ↦ isoMk (Algebra.TensorProduct.lid _ _)) <| fun {A B} f ↦ by
113113 dsimp [baseChange]
@@ -131,7 +131,7 @@ def FiniteEtale.finiteSpec (k : Type u) [Field k] : (FiniteEtale.{v} k)ᵒᵖ
131131
132132/-- If the geometric point `Ω` factors through `S`, the fiber can be computed after base change
133133to `S`. -/
134- @ [expose, simps! ]
134+ @[expose]
135135def FiniteEtale.fiberIsoBaseChangeFiber :
136136 FiniteEtale.fiber.{v} R Ω ≅
137137 (FiniteEtale.baseChange.{v} R S).op ⋙ FiniteEtale.fiber S Ω :=
@@ -140,7 +140,7 @@ def FiniteEtale.fiberIsoBaseChangeFiber :
140140
141141/-- If `Ω` is separably closed, the fiber functor for finite étale `Ω`-algebras
142142is naturally isomorphic to the (finite) `Spec` functor. -/
143- @ [expose, simps! ]
143+ @[expose]
144144noncomputable
145145def FiniteEtale.fiberIsoFiniteSpec [IsSepClosed Ω] :
146146 FiniteEtale.fiber Ω Ω ≅ FiniteEtale.finiteSpec Ω :=
@@ -149,7 +149,7 @@ def FiniteEtale.fiberIsoFiniteSpec [IsSepClosed Ω] :
149149
150150/-- If `Ω` is separably closed, the fiber `S →ₐ[R] Ω`
151151is isomorphic to the prime spectrum of the base change `Ω ⊗[R] S`. -/
152- @ [expose, simps! ]
152+ @[expose]
153153noncomputable
154154def FiniteEtale.fiberIsoComp [IsSepClosed Ω] :
155155 FiniteEtale.fiber.{v} R Ω ≅
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