Effective Homotopy Method

The main idea of the effective homotopy method is the following: given some Kan simplicial sets $K_1,\dots,K_n$ , a topological constructor $\Phi$ produces a new simplicial set $K$ . If solutions for the homotopical problems of the spaces $K_1,\dots,K_n$ are known, then one should be able to build a solution for the homotopical problem of $K$ , and this construction would allow us to compute the homotopy groups $\pi_*(K)$ .