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Apr 7, 2014 at 13:42 comment added Dmitri Pavlov 1. Yes. A¹-invariance of simplicial presheaves guarantees fibrancy in the A¹-localized model structure, which makes it easy to compute homotopy mapping spaces. 2. The situation in the motivic case is no different from the situation in the purely topological case: unpointed spaces give you unpointed spectra, which are the analogs of torsors over abelian groups in the same way that spectra are analogs of abelian groups.
Feb 11, 2014 at 15:21 history edited Carl CC BY-SA 3.0
corrected spelling, added a line to question.
Jan 25, 2014 at 17:46 history asked Carl CC BY-SA 3.0