Timeline for Decompose an unbounded (cochain) complex in the homotopy category
Current License: CC BY-SA 4.0
6 events
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| Mar 8, 2023 at 13:29 | comment | added | Jeremy Rickard | @R.vanDobbendeBruyn I don’t know a reference, sorry. The way I saw this was not by writing down explicit homotopies, but by the fact that the obvious map from $\rho^{>0}A^\bullet$ to the mapping cone is split monic in each degree, and its cokernel is contractible (being the cone of the identity map on $\cdots\to A^{-2}\to A^{-1}\to 0\to\cdots$. I’m sure you can figure out explicit homotopies from that. | |
| Mar 8, 2023 at 12:26 | comment | added | R. van Dobben de Bruyn | Do you have a reference for the homotopy equivalence $\operatorname{Cone}(\tau^{\leq 0}A^\bullet \to A^\bullet) \simeq \rho^{>0}A^\bullet$? I tried doing something like this, but couldn't find the correct homotopy... | |
| Mar 8, 2023 at 10:03 | vote | accept | CommunityBot | ||
| Mar 8, 2023 at 9:47 | history | edited | Jeremy Rickard | CC BY-SA 4.0 |
typo
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| Mar 8, 2023 at 8:58 | history | edited | Jeremy Rickard | CC BY-SA 4.0 |
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| Mar 8, 2023 at 8:44 | history | answered | Jeremy Rickard | CC BY-SA 4.0 |