Can I overload functions with type-traits?

Question

Let\'s say, I have six types, and they each belong in a conceptual category.
Here is a diagram that shows this:

Answer 1

I think using tag despatch would be easier than SFINAE.

template
struct Category;

template<>
struct Category : std::integral_constant {};
template<>
struct Category : std::integral_constant {};
template<>
struct Category : std::integral_constant {};

template<>
struct Category : std::integral_constant {};
template<>
struct Category : std::integral_constant {};
template<>
struct Category : std::integral_constant {};

template
void foo(std::integral_constant, T x)
{
    // Category 1 types.
}

template
void foo(std::integral_constant, T x)
{
    // Category 2 types.
}

template
void foo(T x)
{
    foo(Category(), x);
}