Timeline for Strøm model structures on the category of simplicial sets
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jan 18 at 11:41 | comment | added | Tom Goodwillie | @Tyrone: Yes, definitely. | |
| Jan 18 at 5:16 | comment | added | Tyrone | I feel that Tim's complete answer should be the accepted answer. I hope this is understandable. | |
| Jan 16 at 22:26 | history | edited | Tom Goodwillie | CC BY-SA 4.0 |
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| Jan 16 at 21:17 | comment | added | Tim Campion | Ok, I’ve added my observations as another answer. I think I’ve closed all the loopholes now. | |
| Jan 16 at 18:26 | comment | added | Tyrone | Try this: acyclic fibrations must be surjective (otherwise there aren't enough cofibrant objects). Thus $\Delta^0$ is cofibrant. On the other hand, $\bigsqcup\Delta^0\rightarrow\bigsqcup\Delta^1$ would be a weak equivalence if both $\Delta^0,\Delta^1$ were cofibrant. Thus $\Delta^1$ is not cofibrant. Thus $\Delta^0\rightarrow\Delta^1$ is not a cofibration. | |
| Jan 16 at 17:31 | history | edited | Tom Goodwillie | CC BY-SA 4.0 |
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| Jan 16 at 16:29 | comment | added | Tom Goodwillie | @Tim Campion: Going back to your first comment, if the map $X\to \Delta^1$ is surjective, that gives you a right inverse, but the right inverse might not be compatible with the maps from $\Delta^0$. | |
| Jan 16 at 14:56 | comment | added | Tom Goodwillie | To say that a morphism $f$ is either a cofibration or a fibration in any model structure is to say that for every weak factorization system $f$ is in either the left class or the right class. FWIW, in $Set$ this means precisely that $f$ is either injective or surjective. | |
| Jan 16 at 13:25 | vote | accept | Tyrone | ||
| Jan 18 at 5:16 | |||||
| Jan 16 at 13:25 | comment | added | Tyrone | I really like this! It's exactly the kind of argument I was hoping to see. I was waiting to accept in case David wanted to address the comments under his answer. Thanks also for your input, Tim! | |
| Jan 16 at 13:09 | history | edited | Tom Goodwillie | CC BY-SA 4.0 |
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| Jan 16 at 13:07 | comment | added | Tom Goodwillie | Oh, good! This completes the argument. | |
| Jan 15 at 12:38 | history | edited | Tom Goodwillie | CC BY-SA 4.0 |
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| Jan 15 at 12:20 | history | answered | Tom Goodwillie | CC BY-SA 4.0 |