Homotopy Theory

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Tomer Schlank

17:30

I'll be bold enough to repost my question, as my child-like optimism forces me to believe that the reference I'm looking for is indeed somewhere in the literature.

Let M be a stable model category enriched in Ch(Ab) and Let M_{\infty} the underline \i- category. Clearly if X is cofibrant and Y is fibrant then the complex Hom_M(X,Y) viewed as a spectrum is the spectral \i-categorical Hom_{M_{\infty}}(X,Y). Is there any reference ?

4 hours later…

Denis Nardin

21:58

@TomerSchlank You need only the statement about mapping spaces (since you know that the suspension is the same by general facts about homotopy colimits), and that should be somewhere in Lurie's HTT?

1 hour later…