The secondary Ext groups of the secondary cohomology of the fibers F_n, F_{nZ}, and F are determined as direct sums of F2, polynomial algebras on h0, and suspended copies of F2 in specific bidegrees.
Nassau, On the secondary Steenrod algebra,New York Journal of Mathematics18(2012), 679–705, available athttps://nyjm.albany.edu/j/2012/18-37v.pdf
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Secondary Ext of the Fiber of $Sq^n$ and the Secondary Adams Spectral Sequence
The secondary Ext groups of the secondary cohomology of the fibers F_n, F_{nZ}, and F are determined as direct sums of F2, polynomial algebras on h0, and suspended copies of F2 in specific bidegrees.