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started a minimum at functor with smash products (the realization of ring spectra in terms of lax monoidal functors)
In the end this is entirely a story about monoids with respect to Day convolution tensor products. I suppose there is room to say this yet a bit more general abstractly than MMSS00 did.
I have been adding stuff to functor with smash products. Mainly I have put in all the infrastructure, specialized to pointed topological enrichment, to fully spell out the Day convolution argument and have it all in one place. After the abstract statement about how FSPs come about, I have now started to fill text into the Examples-section. But this remains telegraphic for the moment.
I have been further editing at functor with smash products. There is now a detailed derivation, from first principles, of “orthogonal FSPs over the orthogonal sphere spectrum” being exactly the monoids with respect to the smash product of orthogonal spectra. At the end there is room to unwind the resulting structure a bit more. But not tonight.
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