File: Mathlib/AlgebraicGeometry/Morphisms/UnderlyingMap.lean

full_name: AlgebraicGeometry.instRespectsIsoSchemeTopologicallyInjective
code: instance : MorphismProperty.RespectsIso (topologically Function.Injective) 
goal: (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => Function.Injective).RespectsIso

full_name: AlgebraicGeometry.injective_isLocalAtTarget
code: instance injective_isLocalAtTarget : IsLocalAtTarget (topologically Function.Injective) 
goal: AlgebraicGeometry.IsLocalAtTarget
  (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => Function.Injective)

full_name: AlgebraicGeometry.Surjective.surj
code: /-- A morphism of schemes is surjective if the underlying map is. -/
@[mk_iff]
class Surjective : Prop where
  surj : Function.Surjective f.1.base
goal: Function.Surjective ⇑f.val.base

full_name: AlgebraicGeometry.Surjective
code: /-- A morphism of schemes is surjective if the underlying map is. -/
@[mk_iff]
class Surjective : Prop where
  surj : Function.Surjective f.1.base
goal: Prop

full_name: AlgebraicGeometry.surjective_iff
code: /-- A morphism of schemes is surjective if the underlying map is. -/
@[mk_iff]
class Surjective : Prop where
  surj : Function.Surjective f.1.base
goal: AlgebraicGeometry.Surjective f ↔ Function.Surjective ⇑f.val.base

full_name: AlgebraicGeometry.surjective_eq_topologically
code: lemma surjective_eq_topologically :
    @Surjective = topologically Function.Surjective 
goal: @AlgebraicGeometry.Surjective =
  AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => Function.Surjective

full_name: AlgebraicGeometry.Scheme.Hom.surjective
code: lemma Scheme.Hom.surjective (f : X.Hom Y) [Surjective f] : Function.Surjective f.1.base 
goal: Function.Surjective ⇑f.val.base

full_name: AlgebraicGeometry.instSurjectiveOfIsIsoScheme
code: instance (priority := 100) [IsIso f] : Surjective f 
goal: AlgebraicGeometry.Surjective f

full_name: AlgebraicGeometry.instSurjectiveCompScheme
code: instance [Surjective f] [Surjective g] : Surjective (f ≫ g) 
goal: AlgebraicGeometry.Surjective (f ≫ g)

full_name: AlgebraicGeometry.Surjective.of_comp
code: lemma Surjective.of_comp [Surjective (f ≫ g)] : Surjective g 
goal: AlgebraicGeometry.Surjective g

full_name: AlgebraicGeometry.Surjective.comp_iff
code: lemma Surjective.comp_iff [Surjective f] : Surjective (f ≫ g) ↔ Surjective g 
goal: AlgebraicGeometry.Surjective (f ≫ g) ↔ AlgebraicGeometry.Surjective g

full_name: AlgebraicGeometry.instRespectsIsoSchemeSurjective
code: instance : MorphismProperty.RespectsIso @Surjective 
goal: CategoryTheory.MorphismProperty.RespectsIso @AlgebraicGeometry.Surjective

full_name: AlgebraicGeometry.surjective_isLocalAtTarget
code: instance surjective_isLocalAtTarget : IsLocalAtTarget @Surjective 
goal: AlgebraicGeometry.IsLocalAtTarget @AlgebraicGeometry.Surjective

full_name: AlgebraicGeometry.instRespectsIsoSchemeTopologicallyIsOpenMap
code: instance : (topologically IsOpenMap).RespectsIso 
goal: (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => IsOpenMap).RespectsIso

full_name: AlgebraicGeometry.isOpenMap_isLocalAtTarget
code: instance isOpenMap_isLocalAtTarget : IsLocalAtTarget (topologically IsOpenMap) 
goal: AlgebraicGeometry.IsLocalAtTarget
  (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => IsOpenMap)

full_name: AlgebraicGeometry.instRespectsIsoSchemeTopologicallyIsClosedMap
code: instance : (topologically IsClosedMap).RespectsIso 
goal: (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => IsClosedMap).RespectsIso

full_name: AlgebraicGeometry.isClosedMap_isLocalAtTarget
code: instance isClosedMap_isLocalAtTarget : IsLocalAtTarget (topologically IsClosedMap) 
goal: AlgebraicGeometry.IsLocalAtTarget
  (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => IsClosedMap)

full_name: AlgebraicGeometry.instRespectsIsoSchemeTopologicallyEmbedding
code: instance : (topologically Embedding).RespectsIso 
goal: (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => Embedding).RespectsIso

full_name: AlgebraicGeometry.embedding_isLocalAtTarget
code: instance embedding_isLocalAtTarget : IsLocalAtTarget (topologically Embedding) 
goal: AlgebraicGeometry.IsLocalAtTarget
  (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => Embedding)

full_name: AlgebraicGeometry.instRespectsIsoSchemeTopologicallyOpenEmbedding
code: instance : (topologically OpenEmbedding).RespectsIso 
goal: (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => OpenEmbedding).RespectsIso

full_name: AlgebraicGeometry.openEmbedding_isLocalAtTarget
code: instance openEmbedding_isLocalAtTarget : IsLocalAtTarget (topologically OpenEmbedding) 
goal: AlgebraicGeometry.IsLocalAtTarget
  (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => OpenEmbedding)

full_name: AlgebraicGeometry.instRespectsIsoSchemeTopologicallyClosedEmbedding
code: instance : (topologically ClosedEmbedding).RespectsIso 
goal: (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => ClosedEmbedding).RespectsIso

full_name: AlgebraicGeometry.closedEmbedding_isLocalAtTarget
code: instance closedEmbedding_isLocalAtTarget : IsLocalAtTarget (topologically ClosedEmbedding) 
goal: AlgebraicGeometry.IsLocalAtTarget
  (AlgebraicGeometry.topologically fun {α β} [TopologicalSpace α] [TopologicalSpace β] => ClosedEmbedding)