File: Mathlib/Topology/Category/TopCommRingCat.lean

full_name: TopCommRingCat.isTopologicalSpace
code: /-- A bundled topological commutative ring. -/
structure TopCommRingCat where
  /-- carrier of a topological commutative ring. -/
  α : Type u
  [isCommRing : CommRing α]
  [isTopologicalSpace : TopologicalSpace α]
  [isTopologicalRing : TopologicalRing α]
goal: TopologicalSpace self.α

full_name: TopCommRingCat.isTopologicalRing
code: /-- A bundled topological commutative ring. -/
structure TopCommRingCat where
  /-- carrier of a topological commutative ring. -/
  α : Type u
  [isCommRing : CommRing α]
  [isTopologicalSpace : TopologicalSpace α]
  [isTopologicalRing : TopologicalRing α]
goal: TopologicalRing self.α

full_name: TopCommRingCat
code: /-- A bundled topological commutative ring. -/
structure TopCommRingCat where
  /-- carrier of a topological commutative ring. -/
  α : Type u
  [isCommRing : CommRing α]
  [isTopologicalSpace : TopologicalSpace α]
  [isTopologicalRing : TopologicalRing α]
goal: Type (u + 1)

full_name: TopCommRingCat.isCommRing
code: /-- A bundled topological commutative ring. -/
structure TopCommRingCat where
  /-- carrier of a topological commutative ring. -/
  α : Type u
  [isCommRing : CommRing α]
  [isTopologicalSpace : TopologicalSpace α]
  [isTopologicalRing : TopologicalRing α]
goal: CommRing self.α

full_name: TopCommRingCat.α
code: /-- A bundled topological commutative ring. -/
structure TopCommRingCat where
  /-- carrier of a topological commutative ring. -/
  α : Type u
  [isCommRing : CommRing α]
  [isTopologicalSpace : TopologicalSpace α]
  [isTopologicalRing : TopologicalRing α]
goal: Type u

full_name: TopCommRingCat.instInhabited
code: instance : Inhabited TopCommRingCat 
goal: Inhabited TopCommRingCat

full_name: TopCommRingCat.instCoeSortType
code: instance : CoeSort TopCommRingCat (Type u) 
goal: CoeSort TopCommRingCat (Type u)

full_name: TopCommRingCat.instCategory
code: instance : Category TopCommRingCat.{u} 
goal: CategoryTheory.Category.{u, u + 1} TopCommRingCat

full_name: TopCommRingCat.instConcreteCategory
code: instance : ConcreteCategory TopCommRingCat.{u} 
goal: CategoryTheory.ConcreteCategory TopCommRingCat

full_name: TopCommRingCat.of
code: /-- Construct a bundled `TopCommRingCat` from the underlying type and the appropriate typeclasses.
-/
def of (X : Type u) [CommRing X] [TopologicalSpace X] [TopologicalRing X] : TopCommRingCat 
goal: TopCommRingCat

full_name: TopCommRingCat.coe_of
code: @[simp]
theorem coe_of (X : Type u) [CommRing X] [TopologicalSpace X] [TopologicalRing X] :
    (of X : Type u) = X 
goal: (TopCommRingCat.of X).α = X

full_name: TopCommRingCat.forgetTopologicalSpace
code: instance forgetTopologicalSpace (R : TopCommRingCat) :
    TopologicalSpace ((forget TopCommRingCat).obj R) 
goal: TopologicalSpace ((CategoryTheory.forget TopCommRingCat).obj R)

full_name: TopCommRingCat.forgetCommRing
code: instance forgetCommRing (R : TopCommRingCat) : CommRing ((forget TopCommRingCat).obj R) 
goal: CommRing ((CategoryTheory.forget TopCommRingCat).obj R)

full_name: TopCommRingCat.forgetTopologicalRing
code: instance forgetTopologicalRing (R : TopCommRingCat) :
    TopologicalRing ((forget TopCommRingCat).obj R) 
goal: TopologicalRing ((CategoryTheory.forget TopCommRingCat).obj R)

full_name: TopCommRingCat.hasForgetToCommRingCat
code: instance hasForgetToCommRingCat : HasForget₂ TopCommRingCat CommRingCat 
goal: CategoryTheory.HasForget₂ TopCommRingCat CommRingCat

full_name: TopCommRingCat.forgetToCommRingCatTopologicalSpace
code: instance forgetToCommRingCatTopologicalSpace (R : TopCommRingCat) :
    TopologicalSpace ((forget₂ TopCommRingCat CommRingCat).obj R) 
goal: TopologicalSpace ↑((CategoryTheory.forget₂ TopCommRingCat CommRingCat).obj R)

full_name: TopCommRingCat.hasForgetToTopCat
code: /-- The forgetful functor to `TopCat`. -/
instance hasForgetToTopCat : HasForget₂ TopCommRingCat TopCat 
goal: CategoryTheory.HasForget₂ TopCommRingCat TopCat

full_name: TopCommRingCat.forgetToTopCatCommRing
code: instance forgetToTopCatCommRing (R : TopCommRingCat) :
    CommRing ((forget₂ TopCommRingCat TopCat).obj R) 
goal: CommRing ↑((CategoryTheory.forget₂ TopCommRingCat TopCat).obj R)

full_name: TopCommRingCat.forgetToTopCatTopologicalRing
code: instance forgetToTopCatTopologicalRing (R : TopCommRingCat) :
    TopologicalRing ((forget₂ TopCommRingCat TopCat).obj R) 
goal: TopologicalRing ↑((CategoryTheory.forget₂ TopCommRingCat TopCat).obj R)

full_name: TopCommRingCat.instReflectsIsomorphismsTopCatForget₂
code: /-- The forgetful functors to `Type` do not reflect isomorphisms,
but the forgetful functor from `TopCommRingCat` to `TopCat` does.
-/
instance : (forget₂ TopCommRingCat.{u} TopCat.{u}).ReflectsIsomorphisms 
goal: (CategoryTheory.forget₂ TopCommRingCat TopCat).ReflectsIsomorphisms