  In the present work, we realize the space of 2-string links $\mathcal{L}$ as
a free algebra over a colored operad denoted $\mathcal{SCL}$ (for "Swiss-Cheese
for links"). This result extends works of Burke and Koytcheff about the
quotient of $\mathcal{L}$ by its center and is compatible with Budney's
freeness theorem for long knots. From an algebraic point of view, our main
result refines Blaire, Burke and Koytcheff's theorem on the monoid of isotopy
classes of string links. Topologically, it expresses the homotopy type of the
isotopy class of a 2-string link in terms of the homotopy types of the classes
of its prime factors.
