Timeline for When is the projective model structure cartesian? When is the internal hom invariant?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 29, 2015 at 10:18 | history | edited | David White | CC BY-SA 3.0 |
fixed typos
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| Mar 7, 2013 at 15:15 | vote | accept | Chris Schommer-Pries | ||
| Mar 6, 2013 at 19:52 | answer | added | Charles Rezk | timeline score: 4 | |
| Mar 6, 2013 at 16:14 | answer | added | David White | timeline score: 7 | |
| Mar 6, 2013 at 14:51 | answer | added | Peter May | timeline score: 4 | |
| Mar 6, 2013 at 11:01 | comment | added | Karol Szumiło |
One sufficient condition is that $D$ has coproducts (and of course that $\mathcal{M}$ is cartesian itself). Then the pushout product of generating projective cofibrations of $\mathcal{M}^D$ is a cofibration in $\mathcal{M}$ tensored with a representable copresheaf on $D$ so it is again a projective cofibration. This handles Segal's $\Gamma$ and the site of smooth manifolds (if we allow disconnected manifolds with components of varying dimensions).
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| Mar 6, 2013 at 10:40 | history | edited | Chris Schommer-Pries | CC BY-SA 3.0 |
of
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| Mar 6, 2013 at 10:09 | history | asked | Chris Schommer-Pries | CC BY-SA 3.0 |