File: Mathlib/Order/Category/FinBddDistLat.lean

full_name: FinBddDistLat.toBddDistLat
code: /-- The category of finite distributive lattices with bounded lattice morphisms. -/
structure FinBddDistLat where
  toBddDistLat : BddDistLat
  [isFintype : Fintype toBddDistLat]
goal: BddDistLat

full_name: FinBddDistLat.isFintype
code: /-- The category of finite distributive lattices with bounded lattice morphisms. -/
structure FinBddDistLat where
  toBddDistLat : BddDistLat
  [isFintype : Fintype toBddDistLat]
goal: Fintype ↑self.toBddDistLat.toDistLat

full_name: FinBddDistLat
code: /-- The category of finite distributive lattices with bounded lattice morphisms. -/
structure FinBddDistLat where
  toBddDistLat : BddDistLat
  [isFintype : Fintype toBddDistLat]
goal: Type (u_1 + 1)

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

full_name: FinBddDistLat.instDistribLatticeαToDistLatToBddDistLat
code: instance (X : FinBddDistLat) : DistribLattice X 
goal: DistribLattice ↑X.toBddDistLat.toDistLat

full_name: FinBddDistLat.instBoundedOrderαDistribLatticeToDistLatToBddDistLat
code: instance (X : FinBddDistLat) : BoundedOrder X 
goal: BoundedOrder ↑X.toBddDistLat.toDistLat

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

full_name: FinBddDistLat.of'
code: /-- Construct a bundled `FinBddDistLat` from a `Nonempty` `BoundedOrder` `DistribLattice`. -/
def of' (α : Type*) [DistribLattice α] [Fintype α] [Nonempty α] : FinBddDistLat 
goal: FinBddDistLat

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

full_name: FinBddDistLat.largeCategory
code: instance largeCategory : LargeCategory FinBddDistLat 
goal: CategoryTheory.LargeCategory FinBddDistLat

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

full_name: FinBddDistLat.hasForgetToBddDistLat
code: instance hasForgetToBddDistLat : HasForget₂ FinBddDistLat BddDistLat 
goal: CategoryTheory.HasForget₂ FinBddDistLat BddDistLat

full_name: FinBddDistLat.hasForgetToFinPartOrd
code: instance hasForgetToFinPartOrd : HasForget₂ FinBddDistLat FinPartOrd 
goal: CategoryTheory.HasForget₂ FinBddDistLat FinPartOrd

full_name: FinBddDistLat.Iso.mk_hom_toLatticeHom_toSupHom_toFun
code: /-- Constructs an equivalence between finite distributive lattices from an order isomorphism
between them. -/
@[simps]
def Iso.mk {α β : FinBddDistLat.{u}} (e : α ≃o β) : α ≅ β 
goal: (FinBddDistLat.Iso.mk e).hom.toSupHom a = e a

full_name: FinBddDistLat.Iso.mk_inv_toLatticeHom_toSupHom_toFun
code: /-- Constructs an equivalence between finite distributive lattices from an order isomorphism
between them. -/
@[simps]
def Iso.mk {α β : FinBddDistLat.{u}} (e : α ≃o β) : α ≅ β 
goal: (FinBddDistLat.Iso.mk e).inv.toSupHom a = e.symm a

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

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

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

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

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

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

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

full_name: finBddDistLat_dual_comp_forget_to_bddDistLat
code: theorem finBddDistLat_dual_comp_forget_to_bddDistLat :
    FinBddDistLat.dual ⋙ forget₂ FinBddDistLat BddDistLat =
      forget₂ FinBddDistLat BddDistLat ⋙ BddDistLat.dual 
goal: FinBddDistLat.dual ⋙ CategoryTheory.forget₂ FinBddDistLat BddDistLat =
  CategoryTheory.forget₂ FinBddDistLat BddDistLat ⋙ BddDistLat.dual