Am I mixed up? Let me see.

We have a double complex with one differential increasing

and the other decreasing

This gives me single differential

of definite degree (say +1) if the total degree is taken to be .

So if both and ranged in this gives degrees in all of .

And I'd think this is what I get from forming the chain complex of a cosimplicial simplicial abelian group: a chain complex () of cochain complexes ().

Do you agree?

]]>But the totalization functor in either the second or in the third quadrant still give unboundedness in one direction only, isn't it ?

]]>can anyone point me to some useful discussion of cosismplicial simplicial abelian groups

and cosimplicial simplicial rings

I guess there should be a Dold-Kan correspondence relating these to *unbounded* (co)chain complexes (that may be nontrivial both in positive as well as in negative degree). I suppose it's kind of straightforward how this should work, but I'd still ike to know of any literature that might discuss this. Anything?