I have polished-up the two references offered here (and copied them also over to homotopy n-type):
Edwin Spanier, p. 25 & §8 of: Algebraic topology, McGraw Hill (1966), Springer (1982) [doi:10.1007/978-1-4684-9322-1]
H. J. Baues, Homotopy Types [pdf], in: I. M. James (ed.), Handbook of Algebraic Topology, North Holland (1995) 1-72 [ISBN:9780080532981, doi:10.1016/B978-0-444-81779-2.X5000-7]