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