Given our one-object category, does the functor \\(F\\) always produce a square out of the elements of the chosen set?

What happens if we change base to \\(\mathbf{Cost}\\)? Do we get a square with sides that have a specific length?

Such squares and other simple geometric shapes and their properties were studied by the ancient Greeks extensively. Can the mathematics of the ancient Greeks be defined as a functor or \\(\mathcal{V}\\)-functor?