Timeline for Characterize algebras of the "topological simplices" operad
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 1 at 15:26 | comment | added | David Spivak | Thanks for reminding me, @DavidWhite. I knew this somewhere in my mind, but I guess I hadn't used it enough to have it handy when confronted with the question. | |
| Feb 16 at 15:01 | comment | added | Tom Leinster | @DavidWhite Right, in that book I'm using nonsymmetric operads only, as per Definition 12.1.1 and the comments between 12.1.2 and 12.1.3. The symmetric operad $\Delta$ is certainly interesting too, but it turns out that the symmetries aren't needed for what I was doing, namely, characterizing entropy operadically. | |
| Feb 15 at 17:12 | comment | added | David White | @DavidSpivak Regarding the $\Sigma$-freeness, I think in Leinster's book this operad is meant as a nonsymmetric operad. If you take the associated symmetric operad, via the operation $\Sigma_n \cdot O(n)$ then you do get a $\Sigma$-free symmetric operad. 12.1.5(i) is the terminal operad, and he definitely means non-symmetric because algebras over the terminal symmetric operad are commutative monoids. The associated $\Sigma$-operad of 12.1.5(i) is $Ass(n) = \Sigma_n$ for all $n$. | |
| Feb 15 at 0:26 | answer | added | Todd Trimble | timeline score: 6 | |
| Feb 13 at 17:51 | comment | added | Connor Malin | I think $\Delta$ is cofibrant as a non-symmetric operad, so I believe one actually expects that the homotopy type of every infinite loop space occurs as a nonsymmetric algebra over it. | |
| Feb 13 at 15:23 | comment | added | David Spivak | I was pointed to Leinster's Entropy and Diversity book, which has a family of such algebras as example 12.1.5.(iv). | |
| Feb 13 at 15:22 | comment | added | David Spivak | Thanks @mme, I removed that part. I was confused because I've read multiple times, and I guess taken it on faith, that polynomial monads correspond to ∑-free operads. I'll have to dig deeper into this claim. Thanks again for pointing this out. | |
| Feb 13 at 15:21 | history | edited | David Spivak | CC BY-SA 4.0 |
removing "∑-free"
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| Feb 12 at 20:08 | comment | added | Ryan Budney | @mme: the trivial group feels snubbed. Yes I am a group! | |
| Feb 12 at 17:51 | comment | added | mme | I don't understand the claim that $\Sigma_n$ acts freely on $\Delta_n$. No group acts freely on $\Delta_n$ by Brouwer's fixed point theorem. | |
| Feb 12 at 17:44 | history | asked | David Spivak | CC BY-SA 4.0 |