Maybe I'm looking at the wrong places, but I can't find a definition of the coboundary map on the cochain complex of abelian cosimplicial groups.

What I have in mind is something similar to the "Moore construction in the
**alternating face map complex** "
for abelian simplicial groups, for example given in
http://ncatlab.org/nlab/show/Moore+complex but this time obviously as a
(co)boundary operator on a cochain complex.

Is there an obstruction to a definition? (I guess not)

If not how is it done? (Definition of the coboundary operator)

Introduction to Homological Algebraa useful crutch for the basics of (co)simplicial stuff in homological algebra, so perhaps that might be worth a look. – Yemon Choi Feb 12 '12 at 4:04