Timeline for How many operad structures are there on the symmetric sequence of simplices / finitely-supported probability measures?
Current License: CC BY-SA 4.0
7 events
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| Jun 25, 2018 at 13:20 | comment | added | James Griffin | The examples so far arise from different choices of structure on the set of non-negative real numbers. For the $\circ_f$ example it is a rig with the structure maps conjugates by f of the usual one. For Neil's example, min and max are the operations. My example is too degenerate to say much about. | |
| Jun 25, 2018 at 11:25 | comment | added | Tim Campion | @Peter That does seem to be a pretty natural salvage to try! | |
| Jun 25, 2018 at 11:24 | comment | added | Peter LeFanu Lumsdaine | Like James Griffin’s example below, this structure is a limit of operad structures that do appear in your classification, if I’m not mistaken: it’s the limit as $n \to \infty$ of $(P, \circ^f)$ where $f$ is the $n$th power map, just as the “max” operation is a limit of the $n$th-power means. So perhaps the structures you suggest might be dense among all operad structures? | |
| Jun 25, 2018 at 11:06 | comment | added | Tim Campion | Oh of course -- you need to look at $f \circ (g_1,\dots, g_n)$ where the arities of the $g_i$ are not all the same. | |
| Jun 25, 2018 at 10:58 | comment | added | Neil Strickland | No, that's not an operad morphism. Try some small examples. This is essentially the fact that the group operation on the fundamental group is not associative before passing to homotopy. | |
| Jun 25, 2018 at 10:51 | comment | added | Tim Campion | I'm a little confused. Isn't there an operad morphism $C \to P$ sending the unique point of $C_n$ to $(1/n,\dots,1/n)$? | |
| Jun 25, 2018 at 8:46 | history | answered | Neil Strickland | CC BY-SA 4.0 |