Timeline for Homotopy coherent space maps induces homotopy coherent chain complex morphisms
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 11, 2021 at 15:44 | comment | added | Andrea Marino | Would you mind to elaborate? Actually I am using the topological nerve model for spaces, and not the "localize-at-homotopy-equivalences" one, so I'd be happy to see this direct map. As far as I see such functor would give in components a simplicial map $Top(X \times \Delta^n, Y) \to DK_n(\tau_{\ge 0} Map(C_* X, C_*Y)) $, which maybe is straightforward but not to a newbie like me :) | |
| Jun 11, 2021 at 11:16 | vote | accept | Andrea Marino | ||
| Jun 11, 2021 at 11:16 | comment | added | Andrea Marino | That's a good alternative also. Thanks! I thought passing to a more concrete model (simplicial) made explicit functors easier to define, but actually quasicategories offer the right flexibility in this case. | |
| Jun 10, 2021 at 16:34 | comment | added | Tyler Lawson | As a remark, in some cases it is better to not try to use a simplicial enrichment on $Ch$. Namely, $Ch(\Bbb Z)$ has a quasicategory associated to it (the differential graded nerve, section 1.3.1 in Higher Algebra) and $C_*$ extends directly to a functor $\mathcal{N}(Spaces) \to \mathcal{N}^{dg}(Ch(\Bbb Z))$. | |
| Jun 10, 2021 at 12:18 | answer | added | Maxime Ramzi | timeline score: 4 | |
| Jun 10, 2021 at 10:32 | history | asked | Andrea Marino | CC BY-SA 4.0 |