Timeline for Confusion about interpretation of internal statement $H\cup G=C$ in a Grothendieck topos
Current License: CC BY-SA 3.0
9 events
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| Oct 21, 2016 at 18:43 | comment | added | Arrow | @AndreasBlass I added a reference. The last sentence on page 148 says "for every $C$ in $\mathsf C$, which I think means restricting to representable sheaves. | |
| Oct 21, 2016 at 18:42 | history | edited | Arrow | CC BY-SA 3.0 |
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| Oct 21, 2016 at 18:33 | comment | added | Andreas Blass | Are you sure about "These should be arrows in the site"? Since the passage you quoted seems to be about general C, not necessarily the associated sheaf of a representable presheaf, I'd be inclined to think all of C, D, H, G are objects in the sheaf topos, not in the underlying site. At some point, the author of that passage seems to retreat from the sheaf topos to the presheaf topos, and the stuff about covering should probably be understood in terms of presheaves. $H$ and $G$ cover $C$ as sheaves iff they locally cover it as presheaves. | |
| Oct 21, 2016 at 18:19 | history | edited | Arrow | CC BY-SA 3.0 |
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| Oct 21, 2016 at 18:18 | comment | added | Arrow | @MikeShulman sorry about that. Still though, I'm not really sure how that resolves my problem. Could you help me with the rest? | |
| Oct 21, 2016 at 17:47 | comment | added | Mike Shulman | Last I checked, the Yoneda embedding does commute with products. | |
| Oct 21, 2016 at 11:09 | comment | added | Arrow | @AndrejBauer it just happens that I'm only interested in internal binary covers of representables :) | |
| Oct 21, 2016 at 11:04 | comment | added | Andrej Bauer | $C$ should be kept general here, shouldn't it? Why are you considering only (the sheafification of) a representable $a(y(C))$? | |
| Oct 21, 2016 at 10:54 | history | asked | Arrow | CC BY-SA 3.0 |