diff --git a/src/Bridges/Constraint/det.jl b/src/Bridges/Constraint/det.jl
index 58b2aaed6c..049b891a55 100644
--- a/src/Bridges/Constraint/det.jl
+++ b/src/Bridges/Constraint/det.jl
@@ -98,6 +98,7 @@ function bridge_constraint(::Type{LogDetBridge{T}}, model,
 end
 
 MOI.supports_constraint(::Type{LogDetBridge{T}}, ::Type{<:Union{MOI.VectorOfVariables, MOI.VectorAffineFunction{T}}}, ::Type{MOI.LogDetConeTriangle}) where T = true
+MOIB.added_constrained_variable_types(::Type{<:LogDetBridge}) = Tuple{DataType}[]
 MOIB.added_constraint_types(::Type{LogDetBridge{T}}, ::Type{<:Union{MOI.VectorOfVariables, MOI.VectorAffineFunction{T}}}, ::Type{MOI.LogDetConeTriangle}) where T = [(MOI.VectorAffineFunction{T}, MOI.PositiveSemidefiniteConeTriangle), (MOI.VectorAffineFunction{T}, MOI.ExponentialCone), (MOI.ScalarAffineFunction{T}, MOI.LessThan{T})]
 
 """
@@ -125,6 +126,7 @@ end
 
 # Attributes, Bridge acting as a model
 MOI.get(b::LogDetBridge, ::MOI.NumberOfVariables) = length(b.Δ) + length(b.l)
+MOI.get(b::LogDetBridge, ::MOI.ListOfVariableIndices) = [b.Δ; b.l]
 MOI.get(b::LogDetBridge{T}, ::MOI.NumberOfConstraints{MOI.VectorAffineFunction{T}, MOI.PositiveSemidefiniteConeTriangle}) where T = 1
 MOI.get(b::LogDetBridge{T}, ::MOI.NumberOfConstraints{MOI.VectorAffineFunction{T}, MOI.ExponentialCone}) where T = length(b.lcindex)
 MOI.get(b::LogDetBridge{T}, ::MOI.NumberOfConstraints{MOI.ScalarAffineFunction{T}, MOI.LessThan{T}}) where T = 1
@@ -194,10 +196,12 @@ function bridge_constraint(::Type{RootDetBridge{T}}, model,
 end
 
 MOI.supports_constraint(::Type{RootDetBridge{T}}, ::Type{<:Union{MOI.VectorOfVariables, MOI.VectorAffineFunction{T}}}, ::Type{MOI.RootDetConeTriangle}) where T = true
+MOIB.added_constrained_variable_types(::Type{<:RootDetBridge}) = Tuple{DataType}[]
 MOIB.added_constraint_types(::Type{RootDetBridge{T}}, ::Type{<:Union{MOI.VectorOfVariables, MOI.VectorAffineFunction{T}}}, ::Type{MOI.RootDetConeTriangle}) where T = [(MOI.VectorAffineFunction{T}, MOI.PositiveSemidefiniteConeTriangle), (MOI.VectorAffineFunction{T}, MOI.GeometricMeanCone)]
 
 # Attributes, Bridge acting as a model
 MOI.get(b::RootDetBridge, ::MOI.NumberOfVariables) = length(b.Δ)
+MOI.get(b::RootDetBridge, ::MOI.ListOfVariableIndices) = b.Δ
 MOI.get(b::RootDetBridge{T}, ::MOI.NumberOfConstraints{MOI.VectorAffineFunction{T}, MOI.PositiveSemidefiniteConeTriangle}) where T = 1
 MOI.get(b::RootDetBridge{T}, ::MOI.NumberOfConstraints{MOI.VectorAffineFunction{T}, MOI.GeometricMeanCone}) where T = 1
 MOI.get(b::RootDetBridge{T}, ::MOI.ListOfConstraintIndices{MOI.VectorAffineFunction{T}, MOI.PositiveSemidefiniteConeTriangle}) where T = [b.sdindex]
diff --git a/src/Bridges/Constraint/flip_sign.jl b/src/Bridges/Constraint/flip_sign.jl
index 271af0f329..311122a883 100644
--- a/src/Bridges/Constraint/flip_sign.jl
+++ b/src/Bridges/Constraint/flip_sign.jl
@@ -10,11 +10,17 @@ abstract type FlipSignBridge{
     T, S1<:MOI.AbstractSet, S2<:MOI.AbstractSet,
     F<:MOI.AbstractFunction, G<:MOI.AbstractFunction} <: AbstractBridge end
 
-function MOI.supports_constraint(::Type{<:FlipSignBridge{T, S1}},
-                                 ::Type{<:MOI.AbstractFunction},
-                                 ::Type{S1}) where {T, S1<:MOI.AbstractSet}
+function MOI.supports_constraint(
+    ::Type{<:FlipSignBridge{T, S1}}, ::Type{<:MOI.AbstractScalarFunction},
+    ::Type{S1}) where {T, S1<:MOI.AbstractScalarSet}
     return true
 end
+function MOI.supports_constraint(
+    ::Type{<:FlipSignBridge{T, S1}}, ::Type{<:MOI.AbstractVectorFunction},
+    ::Type{S1}) where {T, S1<:MOI.AbstractVectorSet}
+    return true
+end
+MOIB.added_constrained_variable_types(::Type{<:FlipSignBridge}) = Tuple{DataType}[]
 function MOIB.added_constraint_types(
     ::Type{<:FlipSignBridge{T, S1, S2, F}}) where {T, S1, S2, F}
     return [(F, S2)]
diff --git a/src/Bridges/Constraint/functionize.jl b/src/Bridges/Constraint/functionize.jl
index 5c9e2d8a9a..47157ce748 100644
--- a/src/Bridges/Constraint/functionize.jl
+++ b/src/Bridges/Constraint/functionize.jl
@@ -19,6 +19,7 @@ end
 MOI.supports_constraint(::Type{ScalarFunctionizeBridge{T}},
                         ::Type{<:MOI.SingleVariable},
                         ::Type{<:MOI.AbstractScalarSet}) where {T} = true
+MOIB.added_constrained_variable_types(::Type{<:ScalarFunctionizeBridge}) = Tuple{DataType}[]
 function MOIB.added_constraint_types(::Type{ScalarFunctionizeBridge{T, S}}) where {T, S}
     return [(MOI.ScalarAffineFunction{T}, S)]
 end
@@ -91,6 +92,7 @@ end
 MOI.supports_constraint(::Type{VectorFunctionizeBridge{T}},
                         ::Type{MOI.VectorOfVariables},
                         ::Type{<:MOI.AbstractVectorSet}) where {T} = true
+MOIB.added_constrained_variable_types(::Type{<:VectorFunctionizeBridge}) = Tuple{DataType}[]
 function MOIB.added_constraint_types(::Type{VectorFunctionizeBridge{T, S}}) where {T, S}
     return [(MOI.VectorAffineFunction{T}, S)]
 end
diff --git a/src/Bridges/Constraint/geomean.jl b/src/Bridges/Constraint/geomean.jl
index c7327634cf..5f3d59bb4a 100644
--- a/src/Bridges/Constraint/geomean.jl
+++ b/src/Bridges/Constraint/geomean.jl
@@ -101,6 +101,7 @@ function MOI.supports_constraint(::Type{GeoMeanBridge{T}},
                                 ::Type{MOI.GeometricMeanCone}) where T
     return true
 end
+MOIB.added_constrained_variable_types(::Type{<:GeoMeanBridge}) = Tuple{DataType}[]
 function MOIB.added_constraint_types(::Type{GeoMeanBridge{T, F, G}}) where {T, F, G}
     return [(F, MOI.LessThan{T}), (G, MOI.RotatedSecondOrderCone)]
 end
@@ -116,6 +117,7 @@ end
 
 # Attributes, Bridge acting as a model
 MOI.get(b::GeoMeanBridge, ::MOI.NumberOfVariables) = length(b.xij)
+MOI.get(b::GeoMeanBridge, ::MOI.ListOfVariableIndices) = b.xij
 function MOI.get(b::GeoMeanBridge{T, F},
                  ::MOI.NumberOfConstraints{F, MOI.LessThan{T}}) where {T, F}
     return 1 # t ≤ x_{l1}/sqrt(N)
diff --git a/src/Bridges/Constraint/indicator.jl b/src/Bridges/Constraint/indicator.jl
index 132a149fda..8c8a2aa345 100644
--- a/src/Bridges/Constraint/indicator.jl
+++ b/src/Bridges/Constraint/indicator.jl
@@ -16,25 +16,12 @@ struct IndicatorActiveOnFalseBridge{T, F <: MOI.AbstractVectorFunction, S <: MOI
 end
 
 function bridge_constraint(::Type{IndicatorActiveOnFalseBridge{T,F,S}}, model::MOI.ModelLike, f::MOI.VectorAffineFunction{T}, s::IS) where {S <: MOI.AbstractScalarSet, T <: Real, F, IS <: MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO, S}}
-    z1 = f.terms[1].scalar_term.variable_index
-    z2 = MOI.add_variable(model)
-    zo_cons = MOI.add_constraint(model, MOI.SingleVariable(z2), MOI.ZeroOne())
-
+    f_scalars = MOIU.eachscalar(f)
+    z2, zo_cons = MOI.add_constrained_variable(model, MOI.ZeroOne())
     # z1 + z2 == 1
-    dcons = MOI.add_constraint(model,
-        MOI.ScalarAffineFunction(
-            [MOI.ScalarAffineTerm(one(T), z1), MOI.ScalarAffineTerm(one(T), z2)], zero(T),
-        ),
-        MOI.EqualTo(one(T)),
-    )
-    vec_terms2 = [t for t in f.terms if t.output_index == 2]
-    f2 = MOI.VectorAffineFunction(
-        vcat(
-            [MOI.VectorAffineTerm(1, MOI.ScalarAffineTerm(1.0, z2))],
-            vec_terms2,
-        ),
-        f.constants
-    )
+    z1_z2 = MOIU.operate(+, T, f_scalars[1], MOI.SingleVariable(z2))
+    dcons = MOIU.normalize_and_add_constraint(model, z1_z2, MOI.EqualTo(one(T)))
+    f2 = MOIU.operate(vcat, T, MOI.SingleVariable(z2), f_scalars[2])
     ci = MOI.add_constraint(model, f2, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(s.set))
     return IndicatorActiveOnFalseBridge{T,F,S}(z2, zo_cons, dcons, ci)
 end
@@ -45,8 +32,12 @@ function MOI.supports_constraint(::Type{<:IndicatorActiveOnFalseBridge{T}},
     return true
 end
 
+function MOIB.added_constrained_variable_types(::Type{<:IndicatorActiveOnFalseBridge})
+    return [(MOI.ZeroOne,)]
+end
 function MOIB.added_constraint_types(::Type{IndicatorActiveOnFalseBridge{T, F, S}}) where {T, F, S}
-    return [(F, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, S})]
+    return [(MOI.ScalarAffineFunction{T}, MOI.EqualTo{T}),
+            (F, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, S})]
 end
 
 function concrete_bridge_type(::Type{<:IndicatorActiveOnFalseBridge{T}},
diff --git a/src/Bridges/Constraint/interval.jl b/src/Bridges/Constraint/interval.jl
index 1c458ba179..1949ebfec6 100644
--- a/src/Bridges/Constraint/interval.jl
+++ b/src/Bridges/Constraint/interval.jl
@@ -15,6 +15,7 @@ function bridge_constraint(::Type{SplitIntervalBridge{T, F}}, model, f::F,
 end
 
 MOI.supports_constraint(::Type{SplitIntervalBridge{T}}, ::Type{<:MOI.AbstractScalarFunction}, ::Type{MOI.Interval{T}}) where T = true
+MOIB.added_constrained_variable_types(::Type{<:SplitIntervalBridge}) = Tuple{DataType}[]
 function MOIB.added_constraint_types(::Type{SplitIntervalBridge{T, F}}) where {T, F}
     return [(F, MOI.GreaterThan{T}), (F, MOI.LessThan{T})]
 end
diff --git a/src/Bridges/Constraint/quad_to_soc.jl b/src/Bridges/Constraint/quad_to_soc.jl
index f98aea5391..3f897c7b9d 100644
--- a/src/Bridges/Constraint/quad_to_soc.jl
+++ b/src/Bridges/Constraint/quad_to_soc.jl
@@ -153,6 +153,7 @@ function MOI.supports_constraint(::Type{QuadtoSOCBridge{T}},
                                                 MOI.GreaterThan{T}}}) where T
     return true
 end
+MOIB.added_constrained_variable_types(::Type{<:QuadtoSOCBridge}) = Tuple{DataType}[]
 function MOIB.added_constraint_types(::Type{QuadtoSOCBridge{T}}) where T
     return [(MOI.VectorAffineFunction{T}, MOI.RotatedSecondOrderCone)]
 end
diff --git a/src/Bridges/Constraint/rsoc.jl b/src/Bridges/Constraint/rsoc.jl
index a1f69a612c..adf063d4b7 100644
--- a/src/Bridges/Constraint/rsoc.jl
+++ b/src/Bridges/Constraint/rsoc.jl
@@ -47,6 +47,7 @@ function MOI.supports_constraint(::Type{RSOCBridge{T}},
                                 ::Type{MOI.RotatedSecondOrderCone}) where T
     return true
 end
+MOIB.added_constrained_variable_types(::Type{<:RSOCBridge}) = Tuple{DataType}[]
 function MOIB.added_constraint_types(::Type{<:RSOCBridge{T, F}}) where {T, F}
     return [(F, MOI.SecondOrderCone)]
 end
diff --git a/src/Bridges/Constraint/scalarize.jl b/src/Bridges/Constraint/scalarize.jl
index 3584c632b5..d725d4395f 100644
--- a/src/Bridges/Constraint/scalarize.jl
+++ b/src/Bridges/Constraint/scalarize.jl
@@ -1,13 +1,7 @@
-const VectorLinearSet = Union{MOI.Zeros, MOI.Nonnegatives, MOI.Nonpositives}
-
-scalar_set_type(::Type{<:MOI.Zeros}, T::Type) = MOI.EqualTo{T}
-scalar_set_type(::Type{<:MOI.Nonpositives}, T::Type) = MOI.LessThan{T}
-scalar_set_type(::Type{<:MOI.Nonnegatives}, T::Type) = MOI.GreaterThan{T}
-
 """
     ScalarizeBridge{T, F, S}
 
-Transforms a constraint `AbstractVectorFunction`-in-`vector_set(S)` where
+Transforms a constraint `AbstractVectorFunction`-in-`vector_set_type(S)` where
 `S <: LPCone{T}` to `F`-in-`S`.
 """
 mutable struct ScalarizeBridge{T, F, S} <: AbstractBridge
@@ -17,7 +11,7 @@ end
 function bridge_constraint(::Type{ScalarizeBridge{T, F, S}},
                            model::MOI.ModelLike,
                            f::MOI.AbstractVectorFunction,
-                           set::VectorLinearSet) where {T, F, S}
+                           set::MOIU.VectorLinearSet) where {T, F, S}
     dimension = MOI.output_dimension(f)
     constants = MOI.constant(f, T)
     new_f = MOIU.scalarize(f, true)
@@ -30,16 +24,17 @@ end
 
 function MOI.supports_constraint(::Type{ScalarizeBridge{T}},
                                  ::Type{<:MOI.AbstractVectorFunction},
-                                 ::Type{<:VectorLinearSet}) where T
+                                 ::Type{<:MOIU.VectorLinearSet}) where T
     return true
 end
+MOIB.added_constrained_variable_types(::Type{<:ScalarizeBridge}) = Tuple{DataType}[]
 function MOIB.added_constraint_types(::Type{ScalarizeBridge{T, F, S}}) where {T, F, S}
     return [(F, S)]
 end
 function concrete_bridge_type(::Type{<:ScalarizeBridge{T}},
                               F::Type{<:MOI.AbstractVectorFunction},
-                              S::Type{<:VectorLinearSet}) where T
-    return ScalarizeBridge{T, MOIU.scalar_type(F), scalar_set_type(S, T)}
+                              S::Type{<:MOIU.VectorLinearSet}) where T
+    return ScalarizeBridge{T, MOIU.scalar_type(F), MOIU.scalar_set_type(S, T)}
 end
 
 # Attributes, Bridge acting as a model
@@ -69,7 +64,7 @@ function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintFunction,
 end
 function MOI.get(::MOI.ModelLike, ::MOI.ConstraintSet,
                  bridge::ScalarizeBridge{T, F, S}) where {T, F, S}
-    return vector_set_type(S)(length(bridge.constants))
+    return MOIU.vector_set_type(S)(length(bridge.constants))
 end
 
 function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintPrimal,
diff --git a/src/Bridges/Constraint/soc_to_psd.jl b/src/Bridges/Constraint/soc_to_psd.jl
index df70e8bb3f..85257f692a 100644
--- a/src/Bridges/Constraint/soc_to_psd.jl
+++ b/src/Bridges/Constraint/soc_to_psd.jl
@@ -66,6 +66,7 @@ _SOCtoPSDaff(f::MOI.VectorOfVariables, ::Type{T}) where T = _SOCtoPSDaff(MOI.Vec
 _SOCtoPSDaff(f::MOI.VectorAffineFunction, ::Type) = _SOCtoPSDaff(f, MOIU.eachscalar(f)[1])
 
 MOI.supports_constraint(::Type{SOCtoPSDBridge{T}}, ::Type{<:Union{MOI.VectorOfVariables, MOI.VectorAffineFunction{T}}}, ::Type{MOI.SecondOrderCone}) where T = true
+MOIB.added_constrained_variable_types(::Type{<:SOCtoPSDBridge}) = Tuple{DataType}[]
 MOIB.added_constraint_types(::Type{SOCtoPSDBridge{T}}, ::Type{<:Union{MOI.VectorOfVariables, MOI.VectorAffineFunction{T}}}, ::Type{MOI.SecondOrderCone}) where T = [(MOI.VectorAffineFunction{T}, MOI.PositiveSemidefiniteConeTriangle)]
 
 function MOI.get(model::MOI.ModelLike, a::MOI.ConstraintPrimal, c::SOCtoPSDBridge)
@@ -113,6 +114,7 @@ struct RSOCtoPSDBridge{T, G} <: AbstractBridge
 end
 
 MOI.supports_constraint(::Type{RSOCtoPSDBridge{T}}, ::Type{<:Union{MOI.VectorOfVariables, MOI.VectorAffineFunction{T}}}, ::Type{MOI.RotatedSecondOrderCone}) where T = true
+MOIB.added_constrained_variable_types(::Type{<:RSOCtoPSDBridge}) = Tuple{DataType}[]
 MOIB.added_constraint_types(::Type{<:RSOCtoPSDBridge{T}}, ::Type{<:Union{MOI.VectorOfVariables, MOI.VectorAffineFunction{T}}}, ::Type{MOI.RotatedSecondOrderCone}) where T = [(MOI.VectorAffineFunction{T}, MOI.PositiveSemidefiniteConeTriangle)]
 function concrete_bridge_type(::Type{<:RSOCtoPSDBridge{T}},
                               G::Type{<:MOI.AbstractVectorFunction},
diff --git a/src/Bridges/Constraint/square.jl b/src/Bridges/Constraint/square.jl
index 8474b642cb..6f9aef8863 100644
--- a/src/Bridges/Constraint/square.jl
+++ b/src/Bridges/Constraint/square.jl
@@ -121,6 +121,7 @@ function MOI.supports_constraint(::Type{SquareBridge{T}},
                                 ::Type{<:MOI.AbstractSymmetricMatrixSetSquare}) where T
     return true
 end
+MOIB.added_constrained_variable_types(::Type{<:SquareBridge}) = Tuple{DataType}[]
 function MOIB.added_constraint_types(::Type{SquareBridge{T, F, G, TT, ST}}) where {T, F, G, TT, ST}
     return [(F, TT), (G, MOI.EqualTo{T})]
 end
diff --git a/src/Bridges/Constraint/vectorize.jl b/src/Bridges/Constraint/vectorize.jl
index dd970bbd64..613e74557f 100644
--- a/src/Bridges/Constraint/vectorize.jl
+++ b/src/Bridges/Constraint/vectorize.jl
@@ -1,13 +1,3 @@
-const ScalarLinearSet{T} = Union{MOI.EqualTo{T}, MOI.LessThan{T}, MOI.GreaterThan{T}}
-
-vector_set(::MOI.EqualTo) = MOI.Zeros(1)
-vector_set(::MOI.LessThan) = MOI.Nonpositives(1)
-vector_set(::MOI.GreaterThan) = MOI.Nonnegatives(1)
-
-vector_set_type(::Type{<:MOI.EqualTo}) = MOI.Zeros
-vector_set_type(::Type{<:MOI.LessThan}) = MOI.Nonpositives
-vector_set_type(::Type{<:MOI.GreaterThan}) = MOI.Nonnegatives
-
 """
     VectorizeBridge{T, F, S, G}
 
@@ -20,7 +10,7 @@ mutable struct VectorizeBridge{T, F, S, G} <: AbstractBridge
 end
 function bridge_constraint(::Type{VectorizeBridge{T, F, S, G}},
                            model::MOI.ModelLike, g::G,
-                           set::MOI.AbstractScalarSet) where {T, F, S, G}
+                           set::MOIU.ScalarLinearSet{T}) where {T, F, S, G}
     set_constant = MOI.constant(set)
     h = MOIU.operate(-, T, g, set_constant)
     if -set_constant != MOI.constant(h)[1]
@@ -30,24 +20,25 @@ function bridge_constraint(::Type{VectorizeBridge{T, F, S, G}},
                                                 typeof(set)}(constant))
     end
     f = MOIU.operate(vcat, T, h)
-    vector_constraint = MOI.add_constraint(model, f, vector_set(set))
+    vector_constraint = MOI.add_constraint(model, f, S(1))
     return VectorizeBridge{T, F, S, G}(vector_constraint, set_constant)
 end
 
 function MOI.supports_constraint(::Type{VectorizeBridge{T}},
                                 ::Type{<:MOI.AbstractScalarFunction},
-                                ::Type{<:ScalarLinearSet{T}}) where T
+                                ::Type{<:MOIU.ScalarLinearSet{T}}) where T
     return true
 end
+MOIB.added_constrained_variable_types(::Type{<:VectorizeBridge}) = Tuple{DataType}[]
 function MOIB.added_constraint_types(::Type{<:VectorizeBridge{T, F, S}}) where {T, F, S}
     return [(F, S)]
 end
 function concrete_bridge_type(::Type{<:VectorizeBridge{T}},
                               G::Type{<:MOI.AbstractScalarFunction},
-                              S::Type{<:ScalarLinearSet{T}}) where T
+                              S::Type{<:MOIU.ScalarLinearSet{T}}) where T
     H = MOIU.promote_operation(-, T, G, T)
     F = MOIU.promote_operation(vcat, T, H)
-    return VectorizeBridge{T, F, vector_set_type(S), G}
+    return VectorizeBridge{T, F, MOIU.vector_set_type(S), G}
 end
 
 # Attributes, Bridge acting as a model
@@ -73,8 +64,7 @@ function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintPrimal,
     @assert length(x) == 1
     y = x[1]
     status = MOI.get(model, MOI.PrimalStatus(attr.N))
-    if status != MOI.INFEASIBILITY_CERTIFICATE &&
-       status != MOI.NEARLY_INFEASIBILITY_CERTIFICATE
+    if !MOIU.is_ray(status)
        # If it is an infeasibility certificate, it is a ray and satisfies the
        # homogenized problem, see https://github.com/JuliaOpt/MathOptInterface.jl/issues/433
        # Otherwise, we need to add the set constant since the ConstraintPrimal
@@ -97,7 +87,7 @@ function MOI.modify(model::MOI.ModelLike, bridge::VectorizeBridge,
                                   [(1, change.new_coefficient)]))
 end
 function MOI.set(model::MOI.ModelLike, ::MOI.ConstraintSet,
-                 bridge::VectorizeBridge, new_set::ScalarLinearSet)
+                 bridge::VectorizeBridge, new_set::MOIU.ScalarLinearSet)
     bridge.set_constant = MOI.constant(new_set)
     MOI.modify(model, bridge.vector_constraint,
                MOI.VectorConstantChange([-bridge.set_constant]))
@@ -111,5 +101,5 @@ function MOI.get(model::MOI.ModelLike, attr::MOI.ConstraintFunction,
 end
 function MOI.get(model::MOI.ModelLike, ::MOI.ConstraintSet,
                  bridge::VectorizeBridge{T, F, S}) where {T, F, S}
-    return scalar_set_type(S, T)(bridge.set_constant)
+    return MOIU.scalar_set_type(S, T)(bridge.set_constant)
 end
diff --git a/src/Utilities/sets.jl b/src/Utilities/sets.jl
index f23ed8c604..63330d5b32 100644
--- a/src/Utilities/sets.jl
+++ b/src/Utilities/sets.jl
@@ -19,3 +19,14 @@ end
 function shift_constant(set::MOI.Interval, offset)
     return MOI.Interval(set.lower + offset, set.upper + offset)
 end
+
+const ScalarLinearSet{T} = Union{MOI.EqualTo{T}, MOI.LessThan{T}, MOI.GreaterThan{T}}
+const VectorLinearSet = Union{MOI.Zeros, MOI.Nonnegatives, MOI.Nonpositives}
+
+vector_set_type(::Type{<:MOI.EqualTo}) = MOI.Zeros
+vector_set_type(::Type{<:MOI.LessThan}) = MOI.Nonpositives
+vector_set_type(::Type{<:MOI.GreaterThan}) = MOI.Nonnegatives
+
+scalar_set_type(::Type{<:MOI.Zeros}, T::Type) = MOI.EqualTo{T}
+scalar_set_type(::Type{<:MOI.Nonpositives}, T::Type) = MOI.LessThan{T}
+scalar_set_type(::Type{<:MOI.Nonnegatives}, T::Type) = MOI.GreaterThan{T}
diff --git a/test/Bridges/Constraint/det.jl b/test/Bridges/Constraint/det.jl
index 3700b280b9..4f5164858b 100644
--- a/test/Bridges/Constraint/det.jl
+++ b/test/Bridges/Constraint/det.jl
@@ -1,3 +1,16 @@
+using Test
+
+using MathOptInterface
+const MOI = MathOptInterface
+const MOIT = MathOptInterface.Test
+const MOIU = MathOptInterface.Utilities
+const MOIB = MathOptInterface.Bridges
+
+include("../utilities.jl")
+
+mock = MOIU.MockOptimizer(MOIU.Model{Float64}())
+config = MOIT.TestConfig()
+
 @testset "LogDet" begin
     bridged_mock = MOIB.Constraint.LogDet{Float64}(mock)
     mock.optimize! = (mock::MOIU.MockOptimizer) -> MOIU.mock_optimize!(mock, [0, 1, 0, 1, 1, 0, 1, 0, 0, 1])