Mutlu, APorter, T2024-07-182024-07-180920-3036http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/5027Following Ellis, we investigate the notion of totally free crossed square and related squared complexes. It is shown how to interpret the information in a free simplicial group given with a choice of CW-basis, in terms of the data for a totally free crossed square. Results of Ellis then apply to give a description in terms of tensor products of crossed modules. The paper ends with a purely algebraic derivation of a result of Brown and Loday.EnglishHOMOTOPY-GROUPSMODULESSPACESArticle