On the Singer functor R1 and the functor Fix
Abstract
Lannes' T-functor is used to give a construction of the Singer functor R1 on the category U of unstable modules over the Steenrod algebra A. This leads to a direct proof that the composite functor Fix R1 is naturally equivalent to the identity. Further properties of the functors R1 are deduced, especially when applied to reduced and nilclosed unstable modules.
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