  For commutative algebras there are three important homology theories,
Harrison homology, Andre-Quillen homology and Gamma-homology. In general these
differ, unless one works with respect to a ground field of characteristic zero.
We show that the analogues of these homology theories agree in the category of
pointed commutative monoids in symmetric sequences and that Hochschild homology
always possesses a Hodge decomposition in this setting. In addition we prove
that the category of pointed differential graded commutative monoids in
symmetric sequences has a model structure and that it is Quillen equivalent to
the model category of pointed simplicial commutative monoids in symmetric
sequences.
