Timeline for How do various notions of natural transformation relate to various notions of homotopy in $2Cat$?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 9, 2012 at 8:46 | comment | added | Jonathan Chiche | Ah yes, thanks Mike! I have something to say about that in which you might be interested, I shall write to you privately soon. | |
| Jan 3, 2012 at 18:10 | comment | added | Mike Shulman | The converse is false, but I would say it is because the Gray tensor product $\Delta_1 \otimes_l A$ does not coincide with the lax-functor classifier applied to the cartesian product, $Q_l(\Delta_1 \times A)$. | |
| Jan 3, 2012 at 9:07 | vote | accept | Jonathan Chiche | ||
| Jan 3, 2012 at 9:07 | comment | added | Jonathan Chiche | Thanks! It is basically what I had in mind, at least for the first two items. The third one is interesting. If I am not mistaken, your answer illustrates the fact that a lax transformation between two strict 2-functors from \mathcal{A} to \mathcal{B} gives a lax functor from \Delta_{1} \times \mathcal{A} to \mathcal{B}, but that the converse is false because the cartesian product with \Delta_{1} does not coincide with the Gray tensor product with \Delta_{1}. Am I right on this point? | |
| Jan 2, 2012 at 18:06 | history | answered | Mike Shulman | CC BY-SA 3.0 |