It's interesting that what you come up with is basically the sum of symmetric functions. I guess I'll trust you that this isn't an FGL. :-)

That is to say, the fact that it's not (at least around me) first talked about in that way seems to be historical.

If you're interested in AG, you may be interested to know that descent data is in fact controlled by a coalgebra and its comodules. I'm hardly an authority on the subject, but this seems to be purely a historical accident and not necessarily the "natural" way of things.

I don't think rudeness is really necessary. One of the things that I really like about this site is that one can ask questions (about things that might be frighteningly "obvious" to others) without being verbally cut-down. Though this may the norm in certain realms of academia, there's no reason for it to be.

sorry didn't mean for this to get bumped up to the top... not a very interesting question.

Thanks everyone for your answers. I understand this is an elementary question and perhaps MO was not an appropriate place to bring it up. But there seem to be a lot of simple facts in algebraic topology that are known about spaces and that people feel are obviously true about spectra, but struggle to completely and fully "prove" with all the relevant diagrams when pressed for it. Perhaps this is not one of those things, I don't know. As always, from a humble neophyte, thanks.

I think there might be a difference in our pagination. The paper I'm looking at by that title only has 31 pages.