Timeline for Cofinality for natural transformations
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2020 at 5:07 | comment | added | Emily | @RoaldKoudenburg Hmm... I think the paper answers a different question, which is related to this one. Namely, referring to the very first diagram in p. 2 there, I think my question would correspond to taking $F=\mathrm{id}$ and studying when the induced morphism between co/limits is an iso. From what I understand, however, Paré is studying what would be necessary to have a morphism, not necessarily an iso, between the co/limits. In any case, the paper looks very interesting! Thanks for the pointer :) | |
| Sep 2, 2020 at 17:44 | comment | added | Roald Koudenburg | Robert Paré's Morphisms of colimits might be relevant? | |
| Aug 31, 2020 at 7:34 | comment | added | Zhen Lin | I doubt it. If anything it may be more important to look at the diagram shape $\mathcal{C}$. For instance, if $\mathcal{C}$ has a cofinal full subcategory then you know that the components of the diagram outside that subcategory don't matter. | |
| Aug 31, 2020 at 5:51 | comment | added | Emily | @ZhenLin Thanks! If we impose nice conditions on $\mathcal{D}$ (say being a topos or the category of models of a finite limits theory, etc.), then would “cofinal natural transformations” admit useful characterisations? | |
| Aug 31, 2020 at 1:53 | comment | added | Zhen Lin | This is a right orthogonality condition. As such it is closed under composition and retracts and limits and has the 2-out-of-6 property. If $\mathcal{D}$ is, say, accessible then you only need to check the condition against a small set of objects. I don’t think there’s much more that can be said in this generality, since it depends on $\mathcal{D}$, unlike cofinality of functors. | |
| Aug 30, 2020 at 23:16 | history | edited | Emily | CC BY-SA 4.0 |
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| Aug 30, 2020 at 23:07 | history | edited | Emily | CC BY-SA 4.0 |
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| Aug 30, 2020 at 22:59 | history | asked | Emily | CC BY-SA 4.0 |