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Is it true that (modulo connectivity hypotheses perhaps) $$ \mathrm{Fib}(f) < \mathrm{Fib}(g) $$ implies $$ \mathrm{Fib}(\Sigma f) < \mathrm{Fib}(\Sigma g)? $$

A class $\mathcal{C}$ of pointed spaces is strongly closed if it is closed under weak equivalence, pointed homotopy colimit, and extension by fibrations. We write $X<Y$ if every strongly closed class containing $X$ also contains $Y$.

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    $\begingroup$ I'm not sure what $<$ means, but maybe not. What about cases where $\Sigma f$ is nullhomotopic? $\endgroup$
    – Tom Goodwillie
    Commented Jul 10, 2017 at 18:55
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    $\begingroup$ Isn't there a work by Dror-Farjoun or Chacolski somewhat related to this? $\endgroup$
    – user43326
    Commented Jul 12, 2017 at 16:25
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    $\begingroup$ Yes, those are among the biggest names in this subject. I haven't found this question addressed in the literature, though. $\endgroup$
    – Jeff Strom
    Commented Jul 12, 2017 at 17:50

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