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Jun 21, 2017 at 4:19 history edited Omar Antolín-Camarena CC BY-SA 3.0
fixed commutative diagram
Nov 18, 2009 at 16:04 history edited S. Carnahan CC BY-SA 2.5
diagram
Nov 18, 2009 at 16:03 comment added Mark Hovey Yes, I think Theo is exactly right. In homotopy categories that come from a monoidal model category, commuting S^m (the m-fold suspension of the unit) past S^n always introduces a sign of (-1)^{mn}. This was a conjecture in my model categories book that was resolved by Denis-Charles Cisinski. Essentially one should think of monoidal model categories as algebras over simplicial sets, so whatever happens in simplicial sets to the unit will also happen in any monoidal model category.
Nov 18, 2009 at 15:57 history edited S. Carnahan CC BY-SA 2.5
Mayer-Vietoris
Nov 18, 2009 at 15:31 comment added S. Carnahan Suspension shifts the dimension of singular chains up by one. One then runs into orientation considerations when gluing (as in Eric's question), and it changes their parity when looking at products.
Nov 18, 2009 at 6:30 comment added Theo Johnson-Freyd Ah, so maybe the point is that we should think of the suspension as an "odd" operation, that somehow got (super)commuted past something? (co)homology theories are basically super, no?
Nov 18, 2009 at 5:32 history answered S. Carnahan CC BY-SA 2.5