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I have started a page compactly generated model category. But this is at best “under construction” (I have added a warning). I first just wanted to record Jardine’s definition referred to there. But I find something weird at least in the notation he has (he must mean homotopy colimits in the simplicial localization instead of plain colimits on homotopy hom-sets?!), and I don’t seem to find two different autrhors that agree on all the ingredients.
I’ll leave the entry in this unsatisfactory state for the moment. There is a warning.
Why would he require it for homotopy colimits? That’s not the point of that condition.
I mean… the reason why he does it that way is only obvious if you actually read through the whole paper, because it does actually make sense.
I guess you are right. I should buckle down to sort out in the entry all the different definitions. Or you should! ;-)
It seems like May, Mandell, Shipley, and Schwede are using it to mean something very different.
Yes, it’s a pain.
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