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Nov 22, 2019 at 21:25 comment added Kevin Carlson @HarryGindi I think adding projections lets us avoid your concern; see my edit.
Nov 22, 2019 at 21:24 history edited Kevin Carlson CC BY-SA 4.0
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Nov 22, 2019 at 20:21 comment added Kevin Carlson @HarryGindi Yes, thanks, I let myself slip into talking about a slightly different problem.
Nov 22, 2019 at 20:21 history edited Kevin Carlson CC BY-SA 4.0
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Nov 21, 2019 at 22:15 comment added Harry Gindi A comment: The thing you need is that the multiplication and unit (A_2 structure) don't support any A_4 structure but do support an A_3 structure. I'm not sure if this is true in this case, since we might connive to pick isos such that the diagram commutes by some application of the axiom of choice. Can you show that this isn't possible? The Stasheff example establishes this by showing that an A_4 structure exists on a space but no A_5 structure exists whatsoever, not just that no A_5 structure exists extending that A_4 structure.
Nov 21, 2019 at 18:04 history answered Kevin Carlson CC BY-SA 4.0