For a pointed topological space , we use an inductive construction of a simplicial resolution of by wedges of spheres to construct a “higher homotopy structure” for (in terms of chain complexes of spaces). This structure is then used to define a collection of higher homotopy invariants which suffice to recover up to weak equivalence. It can also be used to distinguish between different maps which induce the same morphism .
David Blanc. Mark W Johnson. James M Turner. "Higher homotopy invariants for spaces and maps." Algebr. Geom. Topol. 21 (5) 2425 - 2488, 2021. https://doi.org/10.2140/agt.2021.21.2425