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Jan 18, 2015 at 20:38 comment added Ulrich Pennig For the record: The "commutation of colimits"-theorem that is needed in this situation is phrased as Corollary 4.2.3.10 in Higher Topos Theory. In fact, the Mayer-Vietoris setup is used as a motivating example in the beginning of the chapter (which reminds me that I need to take a closer look at that book! :-)
Jan 6, 2015 at 23:46 vote accept Ulrich Pennig
Jan 6, 2015 at 21:47 comment added Qiaochu Yuan Unfortunately I'm not at all familiar with May-Sigurdsson. Maybe ask that as a separate question?
Jan 5, 2015 at 12:27 comment added Ulrich Pennig Thanks! Is there a way to see directly that the definition of the Thom spectrum in May and Sigurdsson (which is proven to be equivalent to the above one in the paper mentioned in the question) is compatible with homotopy colimits?
Jan 5, 2015 at 11:28 history edited Qiaochu Yuan CC BY-SA 3.0
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Jan 5, 2015 at 11:19 history answered Qiaochu Yuan CC BY-SA 3.0