Timeline for Homotopical properties of powersets of simplicial sets
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2023 at 20:36 | comment | added | Tim Campion | If $X$ is a set, then $\mathcal P(X)$ is the free infinitary idempotent commutative monoid on $X$. It follows that if $X$ is a simplicial set, then $\mathcal P_\bullet(X)$ is the free infinitary idempotent commutative simplicial monoid on $X$. The unit of $\mathcal P_\bullet(X)$, given by $\emptyset$, is a disjoint basepoint for $\mathcal P_\bullet(X)$. I might guess that $\mathcal P_\bullet(X)$ is weakly homotopy equivalent to $\mathcal P(\pi_0(X))$ (taken discretely). | |
| Feb 21, 2023 at 19:12 | vote | accept | Emily | ||
| Feb 21, 2023 at 19:11 | history | edited | Emily | CC BY-SA 4.0 |
Split the question in two
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| Feb 19, 2023 at 19:20 | answer | added | Dmitri Pavlov | timeline score: 2 | |
| Feb 19, 2023 at 17:27 | history | edited | Emily | CC BY-SA 4.0 |
edited title
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| Feb 19, 2023 at 17:09 | history | asked | Emily | CC BY-SA 4.0 |