# mathlibdocumentation

order.category.BoolAlg

# The category of boolean algebras #

This defines BoolAlg, the category of boolean algebras.

def BoolAlg  :
Type (u_1+1)

The category of boolean algebras.

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Instances for BoolAlg
@[protected, instance]
def BoolAlg.has_coe_to_sort  :
(Type u_1)
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@[protected, instance]
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def BoolAlg.of (α : Type u_1)  :

Construct a bundled BoolAlg from a boolean_algebra.

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@[simp]
theorem BoolAlg.coe_of (α : Type u_1)  :
@[protected, instance]
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Turn a BoolAlg into a BoundedDistribLattice by forgetting its complement operation.

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@[protected, instance]
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@[protected, instance]
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@[protected, instance]
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def BoolAlg.iso.mk {α β : BoolAlg} (e : α ≃o β) :
α β

Constructs an equivalence between boolean algebras from an order isomorphism between them.

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@[simp]
theorem BoolAlg.iso.mk_inv {α β : BoolAlg} (e : α ≃o β) :
@[simp]
theorem BoolAlg.iso.mk_hom {α β : BoolAlg} (e : α ≃o β) :
@[simp]
theorem BoolAlg.dual_obj (X : BoolAlg) :
@[simp]

order_dual as a functor.

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@[simp]

The equivalence between BoolAlg and itself induced by order_dual both ways.

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@[simp]