Spectral Mackey functors are homotopy-coherent versions of ordinary Mackeyfunctors as defined by Dress. We show that they can be described as excisivefunctors on a suitable infinity-category, and we use this to show thatuniversal examples of these objects are given by algebraic K-theory. More importantly, we introduce the unfurling of certain families ofWaldhausen infinity-categories bound together with suitable adjoint pairs offunctors; this construction completely solves the homotopy coherence problemthat arises when one wishes to study the algebraic K-theory of such objects asspectral Mackey functors. Finally, we employ this technology to lay the foundations of equivariantstable homotopy theory for profinite groups and to study fully functorialversions of A-theory, upside-down A-theory, and the algebraic K-theory ofderived stacks.
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