Timeline for In a locally presentable category, is every object (a retract of) the colimit of a chain of smaller objects?
Current License: CC BY-SA 4.0
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| Jan 27, 2021 at 20:28 | comment | added | Tim Campion | I should also ask that the chain be smooth, i.e. that the canonical morphism $\varinjlim_{\beta<\alpha} C_\beta \to C_\alpha$ be an isomorphism for all $\alpha < \lambda$, because the small object argument only interacts well with smooth chains. This is indeed the case in the construction discussed in the answers, with just an iota of extra care (see below). And to clarify from the "Motivation": the small object argument does produce an accessible functor and so in some sense interacts well with highly-filtered colimits; it's just a weaker sense than when it comes to smooth chains. | |
| Sep 1, 2020 at 22:38 | answer | added | Tim Campion | timeline score: 4 | |
| Sep 1, 2020 at 17:21 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Aug 31, 2020 at 17:08 | vote | accept | Tim Campion | ||
| Aug 31, 2020 at 8:29 | answer | added | Jiří Rosický | timeline score: 11 | |
| Aug 30, 2020 at 19:02 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Aug 30, 2020 at 15:53 | history | asked | Tim Campion | CC BY-SA 4.0 |