Mutlu A.Porter T.2025-04-102025-04-102000http://hdl.handle.net/20.500.14701/53369Following 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.Article10.1023/A:1026535602325