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For questions about ring spectra (in homotopy theory).

4 votes

How does one rigorously lift a map $Sp \rightarrow Sp$ of spectra to equivariant spectra?

There are several ways to do this, depending on how much technology one is interested in using. One way to do it is to use the fact that the $\infty$-category of commutative monoid objects in a catego …
Dylan Wilson's user avatar
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16 votes
Accepted

Equivalent definitions of Thom spectra

The details of the comparison are treated in detail in the original ABGHR paper (and then unfortunately split in half across two papers in the updated version), so I'll just try to give a sketch of wh …
Dylan Wilson's user avatar
  • 13.5k
35 votes
Accepted

What is the symmetric monoidal structure on the $(\infty,1)$-category of spectra?

Lurie characterizes the symmetric monoidal structure on $\mathsf{Sp}$ by a universal property (HA.4.8.2.19): it is uniquely determined up to a contractible space of choices by the property that $S^0$ …
Dylan Wilson's user avatar
  • 13.5k