2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59313A 3-dimensional homotopy quantum field theory (HQFT) can be described as a TQFT for surfaces and 3-cobordisms endowed with homotopy classes of maps into a given space. For a group $π$, we introduce a notion of a modular crossed $π$-category and show that such a category gives rise to a 3-dimensional HQFT with target space $K(π,1)$. This includes numerical invariants of 3-dimensional $π$-manifolds and a 2-dimensional homotopy modular functor. We also introduce and discuss a parallel notion of a quasitriangular crossed Hopf $π$-coalgebra.76 pages, no figuresGeometric TopologyQuantum Algebra57Mxxtext