Timeline for Do compactly generated spaces have a more direct definition?
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| Mar 16, 2023 at 19:45 | comment | added | Mike Shulman | Ah, this sounds like the notion that is called stable in D3.3 of the Elephant? And since non-algebraic-geometers generally drop the "quasi" from "compact", is it also common to drop it from "separated"? | |
| Mar 16, 2023 at 14:13 | comment | added | Tim Campion | @MikeShulman Denis T has given the definition; I know I first encountered the concept when reading about how to recover a coherent pretopos from a coherent topos, since a coherent object is one which is quasicompact and quasiseparated. I just looked in Makkai and Reyes Def 9.2.1 and they don't give a name to quasiseparatedness though. But presumably it is defined in SGA. | |
| Mar 16, 2023 at 13:03 | comment | added | Denis T | @MikeShulman I think it should be in SGA4-VII somewhere. Definition is an obvious one mimicking situation for T1 spaces: one says that an object of a topos is quasicompact if every covering (effective epi from coproduct) admits a finite subcovering, and X being quasiseparated means that (binary) fibered products over X preserve quasicompactness. | |
| Mar 16, 2023 at 3:07 | comment | added | Mike Shulman | I've never encountered this "categorical notion which is standard in topos theory". (-: Can you give a reference? | |
| Mar 13, 2023 at 16:53 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Mar 13, 2023 at 16:42 | history | answered | Tim Campion | CC BY-SA 4.0 |