对于平行循环模的Dold-Kan定理
The Dold-Kan theorem for paracyclic modules
Northwestern University（西北大学）
AI总结：
本文通过直接关联Karoubi算子与归一化子复形，证明了平行循环模的Dold-Kan定理。
摘要：
我们研究了平行循环模的未归一化链复形上的Karoubi算子；其在归一化链复形上的限制此前由Dwyer和Kan考虑过，在循环情况下由Cuntz和Quillen研究过。我们通过将Karoubi算子直接与投影到归一化子复形相关联，给出了Dwyer和Kan对于平行循环模的Dold-Kan定理的直接证明。
英文摘要：
We study the Karoubi operator on the unnormalized chain complex of a paracyclic module; its restriction to the normalized chain complex has previously been considered by Dwyer and Kan, and in the cyclic case by Cuntz and Quillen. We obtain a direct proof of the Dold-Kan theorem for paracyclic modules of Dwyer and Kan, by directly relating the Karoubi operator to projection to the normalized subcomplex.
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