File: Mathlib/Order/Category/BddOrd.lean

full_name: BddOrd.toPartOrd
code: /-- The category of bounded orders with monotone functions. -/
structure BddOrd where
  /-- The underlying object in the category of partial orders. -/
  toPartOrd : PartOrd
  [isBoundedOrder : BoundedOrder toPartOrd]
goal: PartOrd

full_name: BddOrd.isBoundedOrder
code: /-- The category of bounded orders with monotone functions. -/
structure BddOrd where
  /-- The underlying object in the category of partial orders. -/
  toPartOrd : PartOrd
  [isBoundedOrder : BoundedOrder toPartOrd]
goal: BoundedOrder ↑self.toPartOrd

full_name: BddOrd
code: /-- The category of bounded orders with monotone functions. -/
structure BddOrd where
  /-- The underlying object in the category of partial orders. -/
  toPartOrd : PartOrd
  [isBoundedOrder : BoundedOrder toPartOrd]
goal: Type (u_1 + 1)

full_name: BddOrd.instCoeSortType
code: instance : CoeSort BddOrd Type* 
goal: CoeSort BddOrd (Type u_1)

full_name: BddOrd.instPartialOrderαToPartOrd
code: instance (X : BddOrd) : PartialOrder X 
goal: PartialOrder ↑X.toPartOrd

full_name: BddOrd.of
code: /-- Construct a bundled `BddOrd` from a `Fintype` `PartialOrder`. -/
def of (α : Type*) [PartialOrder α] [BoundedOrder α] : BddOrd 
goal: BddOrd

full_name: BddOrd.coe_of
code: @[simp]
theorem coe_of (α : Type*) [PartialOrder α] [BoundedOrder α] : ↥(of α) = α 
goal: ↑(BddOrd.of α).toPartOrd = α

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

full_name: BddOrd.largeCategory
code: instance largeCategory : LargeCategory.{u} BddOrd 
goal: CategoryTheory.LargeCategory BddOrd

full_name: BddOrd.instFunLike
code: instance instFunLike (X Y : BddOrd) : FunLike (X ⟶ Y) X Y 
goal: FunLike (X ⟶ Y) ↑X.toPartOrd ↑Y.toPartOrd

full_name: BddOrd.concreteCategory
code: instance concreteCategory : ConcreteCategory BddOrd 
goal: CategoryTheory.ConcreteCategory BddOrd

full_name: BddOrd.hasForgetToPartOrd
code: instance hasForgetToPartOrd : HasForget₂ BddOrd PartOrd 
goal: CategoryTheory.HasForget₂ BddOrd PartOrd

full_name: BddOrd.hasForgetToBipointed
code: instance hasForgetToBipointed : HasForget₂ BddOrd Bipointed 
goal: CategoryTheory.HasForget₂ BddOrd Bipointed

full_name: BddOrd.dual_obj
code: /-- `OrderDual` as a functor. -/
@[simps]
def dual : BddOrd ⥤ BddOrd 
goal: BddOrd.dual.obj X = BddOrd.of (↑X.toPartOrd)ᵒᵈ

full_name: BddOrd.dual_map
code: /-- `OrderDual` as a functor. -/
@[simps]
def dual : BddOrd ⥤ BddOrd 
goal: BddOrd.dual.map a = BoundedOrderHom.dual a

full_name: BddOrd.dual
code: /-- `OrderDual` as a functor. -/
@[simps]
def dual : BddOrd ⥤ BddOrd 
goal: BddOrd ⥤ BddOrd

full_name: BddOrd.Iso.mk_hom
code: /-- Constructs an equivalence between bounded orders from an order isomorphism between them. -/
@[simps]
def Iso.mk {α β : BddOrd.{u}} (e : α ≃o β) : α ≅ β 
goal: (BddOrd.Iso.mk e).hom = ↑e

full_name: BddOrd.Iso.mk
code: /-- Constructs an equivalence between bounded orders from an order isomorphism between them. -/
@[simps]
def Iso.mk {α β : BddOrd.{u}} (e : α ≃o β) : α ≅ β 
goal: α ≅ β

full_name: BddOrd.Iso.mk_inv
code: /-- Constructs an equivalence between bounded orders from an order isomorphism between them. -/
@[simps]
def Iso.mk {α β : BddOrd.{u}} (e : α ≃o β) : α ≅ β 
goal: (BddOrd.Iso.mk e).inv = ↑e.symm

full_name: BddOrd.dualEquiv
code: /-- The equivalence between `BddOrd` and itself induced by `OrderDual` both ways. -/
@[simps functor inverse]
def dualEquiv : BddOrd ≌ BddOrd 
goal: BddOrd ≌ BddOrd

full_name: BddOrd.dualEquiv_functor
code: /-- The equivalence between `BddOrd` and itself induced by `OrderDual` both ways. -/
@[simps functor inverse]
def dualEquiv : BddOrd ≌ BddOrd 
goal: BddOrd.dualEquiv.functor = BddOrd.dual

full_name: BddOrd.dualEquiv_inverse
code: /-- The equivalence between `BddOrd` and itself induced by `OrderDual` both ways. -/
@[simps functor inverse]
def dualEquiv : BddOrd ≌ BddOrd 
goal: BddOrd.dualEquiv.inverse = BddOrd.dual

full_name: bddOrd_dual_comp_forget_to_partOrd
code: theorem bddOrd_dual_comp_forget_to_partOrd :
    BddOrd.dual ⋙ forget₂ BddOrd PartOrd =
    forget₂ BddOrd PartOrd ⋙ PartOrd.dual 
goal: BddOrd.dual ⋙ CategoryTheory.forget₂ BddOrd PartOrd = CategoryTheory.forget₂ BddOrd PartOrd ⋙ PartOrd.dual

full_name: bddOrd_dual_comp_forget_to_bipointed
code: theorem bddOrd_dual_comp_forget_to_bipointed :
    BddOrd.dual ⋙ forget₂ BddOrd Bipointed =
    forget₂ BddOrd Bipointed ⋙ Bipointed.swap 
goal: BddOrd.dual ⋙ CategoryTheory.forget₂ BddOrd Bipointed = CategoryTheory.forget₂ BddOrd Bipointed ⋙ Bipointed.swap