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started something at Bousfield-Friedlander model structure
I have expanded further the definition section, just for completeness
I have turned the discussion of the “strict” model structure on sequential spectra form a half-sentence in the proof of the “stable” model structure into a stand-alone subsection The strict model structure on sequential spectra.
Then I laboriously drew the diagrams explicitly showing that the cofibrations are what they are.
(I thought I had this kind of argument spelled out long ago somewhere at model structure on functors or at Joyal-Tierney calculus, but now I couldn’t find it.)
I have edited the beginning of the proof of the statement (here) of the strict BF-model structure on sequential spectra.
Previously the proof had started out with “consider the transferred model structure on sequential spectra, transferred from $\mathbb{N}$-sequences”. Not only was that lacking the argument for why the model structure exists, but even if one sees that, it turns out not to be the most fruitful perspective.
Better is to see – and that’s how I have edited the proof now – that the category of sequential spectra is equivalently an enriched functor category, and that under this identification the strict BF-model structure is just the projective model structure on enriched functors.
Started adding some basics to a section Properties – Fibrations and cofibrations: 1) CW-spectra are cofibrant and 2) the standard cylinder spectrum over a CW-spectrum is a good cylinder object.
This may need beautifying. But later, not tonight.
okay, that last edit was the last drop, it finally made me go and split off a separate entry model structure on topological sequential spectra from Bousfield-Friedlander model structure (which is in simplicial sets). I had originally hoped that I could just carry the topological variant along with the simplicial one, but it’s getting awkward, and so it better be in its own entry. I’ll be expanding there further.
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