# mathlibdocumentation

order.category.Frame

# The category of frames #

This file defines Frame, the category of frames.

## References #

def Frame  :
Type (u_1+1)

The category of frames.

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Instances for Frame
@[protected, instance]
def Frame.has_coe_to_sort  :
(Type u_1)
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@[protected, instance]
def Frame.order.frame (X : Frame) :
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def Frame.of (α : Type u_1) [order.frame α] :

Construct a bundled Frame from a frame.

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@[simp]
theorem Frame.coe_of (α : Type u_1) [order.frame α] :
(Frame.of α) = α
@[protected, instance]
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@[reducible]
def Frame.hom (α : Type u_1) (β : Type u_2) [order.frame α] [order.frame β] :
Type (max u_1 u_2)

An abbreviation of frame_hom that assumes frame instead of the weaker complete_lattice. Necessary for the category theory machinery.

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

Constructs an isomorphism of frames from an order isomorphism between them.

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@[simp]
theorem Frame.iso.mk_hom {α β : Frame} (e : α ≃o β) :
@[simp]
theorem Frame.iso.mk_inv {α β : Frame} (e : α ≃o β) :
@[simp]
theorem Top_op_to_Frame_obj (X : Topᵒᵖ) :
@[simp]
theorem Top_op_to_Frame_map (X Y : Topᵒᵖ) (f : X Y) :

The forgetful functor from Topᵒᵖ to Frame.

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@[protected, instance]