Timeline for What is the categorical analogue of openness?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 18, 2019 at 19:34 | answer | added | Tim Campion | timeline score: 1 | |
| Sep 9, 2019 at 16:11 | comment | added | Theo Johnson-Freyd | @QiaochuYuan Good point. But permit me to be open-minded? I'm often annoyingly imprecise :) | |
| Sep 8, 2019 at 19:50 | comment | added | Qiaochu Yuan | There are several different kinds of "enoughness" / "density" and they don't always agree, e.g. you might want iterated colimits rather than just colimits or else $\mathbb{Z}$ isn't dense in abelian groups. See e.g. qchu.wordpress.com/2015/05/17/generators for a discussion. | |
| Sep 8, 2019 at 18:00 | comment | added | John Dougherty | Perhaps another example is accessible subcategories of accessible categories, with the compact objects as the dense subset. Accessible subcategories agree about which objects are compact, they are closed under intersection, and the preimage of an accessible subcategory under an accessible functor is also an accessible subcategory. This involves restricting to filtered colimits, though. | |
| Sep 8, 2019 at 17:00 | comment | added | Theo Johnson-Freyd | It's worth reminding that categories have two sometimes-competing "topologies", because they have both limits and colimits. I've somewhat arbitrarily chosen the colimit topology, but note that when an abelian category has, say, "enough injectives", then that's a limit-topology statement, not a colimit-topology statement. | |
| Sep 8, 2019 at 16:58 | history | asked | Theo Johnson-Freyd | CC BY-SA 4.0 |