Corrected the reference to HA. It previously pointed to the wrong section; now it points to the specific theorem containing Lurie’s formulation of the loop-space principle.

]]>A point that confused me for a long time is that the literature about infinite loop spaces isn’t always clear whether or not they are intended to come equipped with a distinguished choice of deloopings.

As I understand, the equivalences with notions of connective spectra and E∞ groups are only for when you equip infinite loop spaces with a distinguished choice of deloopings, so I’ve added language to that effect.

Is there standard language for expressing this? My choice of language is to say “infinite loop space with a choice of deloopings” which feels awkward.

]]>added ISBN:9780691082066 and doi:10.1515/9781400821259 to:

- John Adams,
*Infinite loop spaces*, Hermann Weyl lectures at IAS, Princeton University Press (1978) (ISBN:9780691082066, doi:10.1515/9781400821259)

time for a table. I am experimenting with this here:

A version of this is currently at infinite loop space, but I think I’ll make it an include-entry now

]]>Prompted by an email question that I received, I noted that the entry *infinite loop space* was (and is) in bad shape.

I have now added some references to it and a sentence including the word “$E_\infty$”. Maybe I find time to do a bit more…

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