Timeline for Does stabilization preserve the property of being a full subcategory?
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| Apr 30, 2017 at 11:53 | comment | added | AAK | Generally, stabilization is usually defined as a limit, using a right adjoint functor $v$ for the transition arrows in the tower. Then the answer to your question is yes, provided that the inclusion $F$ commutes with $v$, because limits of fully faithful functors are fully faithful. In the presentable case you can compute this limit as a colimit in the category of presentable $\infty$-categories and left adjoints (with the transition arrows in the tower being the left adjoint of $v$), but beware that this is not the same as the colimit in the category of $\infty$-categories. | |
| Apr 30, 2017 at 0:16 | review | First posts | |||
| Apr 30, 2017 at 0:28 | |||||
| Apr 30, 2017 at 0:12 | history | asked | user109219 | CC BY-SA 3.0 |