Timeline for Verifying a technical lemma regarding homotopy pushouts in the theory of simplicial model categories
Current License: CC BY-SA 2.5
13 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Jul 11, 2010 at 7:46 | comment | added | Harry Gindi | I'd just like to comment that the entire question becomes trivial with the correction. | |
| Jul 11, 2010 at 5:34 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Jul 11, 2010 at 5:07 | vote | accept | Harry Gindi | ||
| Jul 11, 2010 at 1:48 | answer | added | Tom Goodwillie | timeline score: 6 | |
| Jul 11, 2010 at 1:37 | comment | added | Tom Goodwillie | Rereading the question, I find that it looks like you did not write exactly what you meant. I am guessing that $K$ was meant to be the pushout of the simplex and $L$ along the boundary of the simplex -- that is, that $\sigma$ was meant to be the only nondegenerate simplex of $K$ not in $L$. $K$ does not appear in the conclusion. | |
| Jul 10, 2010 at 19:00 | comment | added | Tom Goodwillie | Well, here's something funny: Not only did my comment not use the assumption that the map $A\otimes\Delta^n\to A\otimes \Delta^0$ is a weak equivalence for any object $A$ -- it shows that that assumption is superfluous, because a one-sided inverse $A\otimes\Delta^0\to A\otimes \Delta^n$ is a trivial cofibration. | |
| Jul 10, 2010 at 17:12 | comment | added | Tom Goodwillie | Here's an easy step, which may or may not be in the right direction: You want to show that tensoring with D preserves cofibrations, or equivalently that its right adjoint preserves trivial fibrations. It's clear that tensoring with D preserves trivial cofibrations, or equivalently that its right adjoint preserves fibrations, because that's what (*) says when A is initial and B is D. | |
| Jul 10, 2010 at 7:59 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Jul 10, 2010 at 5:36 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Jul 10, 2010 at 4:57 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Jul 10, 2010 at 4:51 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Jul 10, 2010 at 4:45 | history | asked | Harry Gindi | CC BY-SA 2.5 |