Timeline for Are reflective subcategories of complete infinity categories complete?
Current License: CC BY-SA 3.0
14 events
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| S Sep 23, 2022 at 8:54 | history | suggested | Ken |
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| Sep 23, 2022 at 8:33 | review | Suggested edits | |||
| S Sep 23, 2022 at 8:54 | |||||
| Sep 23, 2022 at 8:02 | answer | added | Ken | timeline score: 0 | |
| Jun 3, 2013 at 17:14 | comment | added | Dylan Wilson | @David: Right, I was being silly :) Proof below... | |
| Jun 3, 2013 at 16:39 | answer | added | Dylan Wilson | timeline score: 4 | |
| Jun 3, 2013 at 14:48 | comment | added | Marc Hoyois | @David: It should be easy to prove that what you get by applying the reflector to the limit in the ambient category is the limit in the subcategory. | |
| Jun 3, 2013 at 11:32 | history | edited | David Carchedi | CC BY-SA 3.0 |
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| Jun 3, 2013 at 11:31 | comment | added | David Carchedi | @Dylan: The proposition says something much simpler: left adjoints preserves colimits and right adjoints preserve limits. I need to knwo that limits exist before I can show they are preserved. | |
| Jun 3, 2013 at 7:54 | comment | added | Dylan Wilson | Why doesn't this follow from HTT 5.2.3.5? | |
| Jul 17, 2012 at 18:11 | comment | added | Mike Shulman | No, Buschi is correct. The inclusion functor of a reflective subcategory is a right adjoint, and hence preserves all limits; it's colimits in the reflective subcategory that you have to apply the reflector to compute. Torsion abelian groups are not a reflective subcategory of abelian groups (what would the reflection of $\mathbb{Z}$ be?). | |
| Jul 17, 2012 at 12:13 | comment | added | Martin Brandenburg | @Buschi: This is not true. You need the reflector. Look, for example, at the category of torsion abelian groups within the category of abelian groups. Besides, David asks about higher categories. | |
| Jul 17, 2012 at 11:20 | comment | added | David Carchedi | So, what you are saying is that applying the reflector is redundant? | |
| Jul 17, 2012 at 11:17 | comment | added | Buschi Sergio | for reflexive (full, replete) subcatgories $\iota: \mathcal{A}\subset\mathcal{C}$ the limits in $A$ are calculate as the limits on the ground category $\mathcal{C}$ (without applyng reflector), infact the inclusion $\iota: \mathcal{A}\subset\mathcal{C}$ create limits (large limits too). WHat do you said is valid for colimits. | |
| Jul 17, 2012 at 10:49 | history | asked | David Carchedi | CC BY-SA 3.0 |