The $ (\infty, 1)$ category $ Sp$ of spectra as defined by Lurie in Higher Algebra has the structure of a symmetric monoidal category. Although I know the definition of symmetric monoidal category in the $ (\infty, 1)$ setting and can reasonably follow Lurie’s arguments in Higher Algebra as to why $ Sp$ has such a structure, I don’t understand it well-enough to think about it intuitively.
So my question is, what does the symmetric monoidal structure on $ Sp$ look like? How is this related to the symmetric monoidal structure on symmetric or orthogonal spectra in the ordinary categorical setting? How may I picture ring spectra and other such objects arising from the monoidal structure?
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