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Hi!
I took a look at the page on pseudonatural transformations today. This doesn’t seem right to me. A natural transformation between functors from C to D involves, for each 0-cell of C, a 1-cell of D; and for each 1-cell of C, an equation between 2-cells of D. By extension, a pseudonatural transformation between pseudofunctors from C to D should involve, for each 0-cell of C, a 1-cell of D; for each 1-cell of C, a 2-cell of D; and for each 2-cell of C, an equation between 2-cells of D. When I’ve needed to use pseudonatural transformations in the past, this is the sort of definition I’ve always used. I can’t see how it would be equivalent to the one given on the nLab page at the moment.
If I’m right, please let me make the changes! I’ve never edited an nLab page before.
Cheers, Jamie.
Right, the tin-can equation is missing on that page.
By the way, to refer to an Lab page here on the forum, just type its title in double square brackets.
Thanks Urs. I’ll edit the page. And thanks for the nLab tip.
’Tin-can’?
If you draw it 3-dimensionally for the standard globular model of 2-categories, the 2-naturality is an identity-filled cylinder “with weld”s. Looks like a tin can.
I have added a sentence that a condfition is missing. If you could maybe fill in the diagram?
By the way, the compositors are currently also missing in the diagrams. As are the associators. But I guess we want to leave them implicit.
I’m not having much luck, unfortunately. I started making the necessary edits, and wanted to preview the page. But it seemed there was no facility for that, so I saved my changes. The page now appears blank. Presumably there’s something wrong with my code. Fishing around, I’ve found a ’Rollback’ command, but I can’t get it to do anything. So, I’m stuck – perhaps someone can help me out.
Is there really no way to preview code changes without saving them? It takes quite a long time to save and re-generate a page, and it creates an unnecessary and distracting history of irrelevant edits. Plus, it’s inconvenient for others if they stumble upon a page in a half-edited state.
Looking at the source view, I see this line just before the table-of-contents incantation:
=--http://ncatlab.org/nlab/edit/pseudonatural+transformation
You might have pasted in the URL accidentally somehow, and maybe that’s what Instiki is choking on. You could try removing it and saving again.
I’m no expert, but I’d assume that previewing wouldn’t be any faster than saving. Instiki doesn’t distinguish between edits made (I think) less than 30 minutes apart, so you needn’t worry about cluttering up the history.
Edit: Yup, that worked.
Thanks Finn!
Instiki’s philosophy is that the “preview” button is labeled “save”. If you don’t like the result, just edit again and change it. Multiple edits by the same person within 30 minutes are counted as one edit.
At first I didn’t like this approach; I wanted a preview button too. But as with some other things about Instiki, gradually I got used to it, and now I edit other wikis in the same way. Most of the time, what I write is okay and then this way saves me from having to push an extra button. It also prevents people from forgetting to push the extra button! If the result isn’t okay, then it’s only one more click to get back to the edit page, which is a click I would have had to make anyway if I were looking at a preview instead.
As Finn says, it seems possible to me that previewing wouldn’t be much faster than saving – but depending on how much of the save time involves trawling the database to update links and redirects in other pages, that might not be true. It would be interesting to find that out.
Anyway, I’ve added an entry about this to the FAQ.
Jamie,
“rollback” works like this: you hit “Rollback” to get the former source code, and then you have to hit “Save” again to replace that for the current version.
This used to confuse me at the beginning, too. One expects that a button called “rollback” actually affects the database. But it does not.
okay, I have now started to fix the entry:
included the functor’s compositors in the statement of the respect of the transformation for composition;
added the naturality condition:
removed the incorrect statement about respect for units and … was too lazy to typo out the correct one, so now it just says “respect for units” there.
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