Subject: Symmetric precubical set
From: Gaucher Philippe <Philippe.Gaucher@pps.jussieu.fr>
Date: Thu, 5 Jul 2007 14:02:28 +0200

Dear all,

Has anyone encoutered something like that: 

The object could be called symmetric precubical set. Here is an example. 
Take 
a topological space X. And K(n)=Top([0,1]^n,X). 

1) The face maps are the usual ones : 
d_i^alpha(f)(x_1,...x_{n-1})f(x_1,...,x_{i-1},alpha,x_i,...,x_{n-1})

2) No degeneracy maps (PREcubical set)

3) AND the operations 
sigma(f)(x_1,...x_n)=f(x_{sigma^{-1}(1)},...,x_{sigma^{-1}(n)}
for all bijections of {1,...,n}.

Question : if yes, what is the name of this object ? Any reference ?

Thanks in advance. pg.