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I am curious to know whether spectra with coefficients as defined in Adams's Blue book be defined to an equivariant setting. In the non-equivariant case, for a spectrum $E$ and an abelian group $A$, one can define the spectrum with coefficients in $A$ by taking the smash product $E\wedge M(A)$, where $M(A)$ is the Moore spectrum.

How can I define a $G$-equivariant spectrum with coefficients?

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  • $\begingroup$ Do you want $G$ go act on $A$? In that case there are obstructions, cf. jstor.org/stable/2154066 $\endgroup$
    – user43326
    Commented Feb 7, 2023 at 17:43
  • $\begingroup$ No, I want to see whether the generalisation of spectrum with coefficients is possible in the equivariant case. I am curious whether there is such a thing as an equivariant spectrum with coefficients. $\endgroup$
    – anon
    Commented Feb 7, 2023 at 18:03
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    $\begingroup$ This was asked at mathoverflow.net/questions/431226/… and answered in the comments. The category of $G$-equivariant spectra (like any stable $\infty$-category) is enriched over the category of spectra, so you can just define $EA=E\wedge M(A)$ again. $\endgroup$
    – Neil Strickland
    Commented Feb 8, 2023 at 12:57

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