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Set Implicit Arguments.
Generalizable All Variables.
Set Asymmetric Patterns.
Set Universe Polymorphism.
Set Printing Universes.
Set Printing All.
Record PreCategory :=
{
Object :> Type;
Morphism : Object -> Object -> Type
}.
Inductive paths A (x : A) : A -> Type := idpath : @paths A x x.
Inductive Unit : Prop := tt. (* Changing this to [Set] fixes things *)
Inductive Bool : Set := true | false.
Definition DiscreteCategory X : PreCategory
:= @Build_PreCategory X
(@paths X).
Definition IndiscreteCategory X : PreCategory
:= @Build_PreCategory X
(fun _ _ => Unit).
Check (IndiscreteCategory Unit).
Check (DiscreteCategory Bool).
Definition NatCategory (n : nat) :=
match n with
| 0 => IndiscreteCategory Unit
| _ => DiscreteCategory Bool
end. (* Error: Universe inconsistency (cannot enforce Set <= Prop). *)
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