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Set Implicit Arguments.
Set Universe Polymorphism.
Generalizable All Variables.
Record SpecializedCategory (obj : Type) :=
{
Object :> _ := obj
}.
Record > Category :=
{
CObject : Type;
UnderlyingCategory :> @SpecializedCategory CObject
}.
Record SpecializedFunctor `(C : @SpecializedCategory objC) `(D : @SpecializedCategory objD) :=
{
ObjectOf :> objC -> objD
}.
Definition Functor (C D : Category) := SpecializedFunctor C D.
Parameter TerminalCategory : SpecializedCategory unit.
Definition focus A (_ : A) := True.
Definition CommaCategory_Object (A : Category) (S : Functor TerminalCategory A) : Type.
assert (Hf : focus ((S tt) = (S tt))) by constructor.
let C1 := constr:(CObject) in
let C2 := constr:(fun C => @Object (CObject C) C) in
unify C1 C2.
progress change CObject with (fun C => @Object (CObject C) C) in *.
simpl in *.
let V := match type of Hf with
| focus ?V => constr:(V)
end
in exact V.
(* Toplevel input, characters 89-96:
Error: Illegal application:
The term "ObjectOf" of type
"forall (objC : Set) (C : SpecializedCategory objC)
(objD : Type) (D : SpecializedCategory objD),
SpecializedFunctor C D -> objC -> objD"
cannot be applied to the terms
"Object TerminalCategory" : "Type"
"TerminalCategory" : "SpecializedCategory unit"
"Object A" : "Type"
"UnderlyingCategory A" : "SpecializedCategory (CObject A)"
"S" : "Functor TerminalCategory A"
"tt" : "unit"
The 1st term has type "Type" which should be coercible to
"Set". *)
Defined.
|
