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Oct 16 at 20:46 comment added Tim Campion @user39598 The derived category of any nonzero ring is an example. See the third paragraph of this answer.
Sep 29 at 15:05 comment added user39598 Do you know of any explicit examples of stable presentable categories that are not stabilizations of a topos? I can image taking a pushout of stabilization of topos (in StPrL) will not be a stabilization of topos in general.
Nov 17, 2022 at 14:37 history edited Tim Campion CC BY-SA 4.0
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Nov 10, 2022 at 22:07 history edited Tim Campion CC BY-SA 4.0
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Nov 10, 2022 at 21:54 history edited Tim Campion CC BY-SA 4.0
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Nov 10, 2022 at 21:47 history answered Tim Campion CC BY-SA 4.0