Timeline for Can skeleta simplify category theory?
Current License: CC BY-SA 2.5
10 events
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| Feb 27, 2018 at 0:06 | comment | added | Yemon Choi | Rolling back the rather superfluous addition of a hyperlink, as there is now no guarantee Ranicki's website/filespace will remain active | |
| Feb 27, 2018 at 0:06 | history | rollback | Yemon Choi |
Rollback to Revision 1
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| S Feb 26, 2018 at 7:12 | history | suggested | Mike Pierce | CC BY-SA 3.0 |
Added a link to the argument in MacLane, hosted on Andrew Ranicki’s website
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| Feb 26, 2018 at 1:10 | review | Suggested edits | |||
| S Feb 26, 2018 at 7:12 | |||||
| Jan 13, 2010 at 20:55 | comment | added | Leonid Positselski | The strictification of the conventional tensor category of vector spaces is also more complicated than the original thing. Generally, my answer does not express any opinion about merits or demerits of strictification (though I'm sure it has both). It is just my impression that strictification is what the question intended to achieve (for whatever purpose). The answer is that skeletons are inadequate to the task, at least, in this one instance (and also generally). | |
| Jan 13, 2010 at 20:29 | comment | added | Noah Snyder | Also I should say that it doesn't make sense to play these two thing against each other: not only is it bad only to think about strictly monoidal categories and bad to only think about skeletal categories, they're both bad for roughly the same reasons. | |
| Jan 13, 2010 at 20:25 | comment | added | Noah Snyder | My question was rhetorical, I know it can be done but actually doing so replaces something very simple with something very complicated. Vec(G, \omega) is G-graded vector spaces with the associator given by \omega. Check out Mueger's notes on tensor categories on the arxiv for more. | |
| Jan 13, 2010 at 19:46 | comment | added | Leonid Positselski | Sorry for my ignorance, but could you give a reference for Vec(G,\omega)? In any event, MacLane explains how to strictify any monoidal category in section XI.3. It involves adding new objects to each isomorphism class rather than removing the old ones. | |
| Jan 13, 2010 at 19:17 | comment | added | Noah Snyder | Though, on the other hand, one might think of this as an argument against thinking about strictly monoidal categories! What's the strictly monoidal version of Vec(G, \omega) for a 3-cocycle \omega? | |
| Jan 13, 2010 at 18:58 | history | answered | Leonid Positselski | CC BY-SA 2.5 |