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Freeness conditions for crossed squares and squared complexes

A. Mutlu·T. Porter
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Abstract

Following Ellis, we investigate the notion of totally free crossed squares and related square 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.

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A. Mutlu, T. Porter. 1999-04-09. Freeness conditions for crossed squares and squared complexes. https://arxiv.org/abs/math/9904041

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