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Comparison: Formal Wirthmüller isomorphism of Fausk-Hu-May vs. Balmer et. al

$\newcommand{\Cc}{\mathcal{C}}$ $\newcommand{\Dd}{\mathcal{D}}$ $\newcommand{\tensor}{\otimes}$ $\DeclareMathOperator{\Sp}{Sp}$ This question is about comparing the approaches for a formal Wirthmüller ...