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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I’ll be preparing here notes for my lectures Categories and Toposes (schreiber), later this month.
In Definition 2.14, clause 3, isn’t that monoidal product rather than cartesian product?
Thanks for catching this, fixed now.
In fact, large parts of text still need to be transferred from -enrichment to arbitrary -enrichment.
finally made it to the discussion of “solid model toposes” in the last section (here). This should set the scope. Still need to expand and polish some bits, but maybe not add any further sections.
It depends what you mean by load. If you mean that all the MathJax is finished, then yes, it takes forever. If you mean that the page is loaded apart from the MathJax, then no, it is not normal after the rendering changes made a couple of months ago; it takes a while only the very first time it is loaded after an edit (this generates the cache). Eventually the latter will be changed as well, so that the loading is always more or less immediate (apart from MathJax).
Pagination could be an interesting idea, though, for the future.
With Firefox it works pleasantly. Firefox (and its derivatives) is the only browser left that has native MathML support, since all other browsers abondened support for it some years ago. That’s what makes the difference in rendering the maths.
I keep thinking we should have a general announcement on Lab pages, that recommends Firefox to the reader.
And we should pray that the Mozillas never ever decide to remove their MathML support, too.
I keep thinking we should have a general announcement on nLab pages, that recommends Firefox to the reader.
Maybe you’re right after all! Maybe others can share their opinion on this; if enough think it a good idea, I will implement it.
That’s [i.e. MathML is] what makes the difference in rendering the maths.
I would say that that’s not quite true. What makes MathJax slow is only that it is client side, i.e. done in the user’s browser, it does not have to do with the use of MathML. What we really need, in my opinion, is a good server side way to produce HTML/CSS for mathematics directly, without using MathML. I am making some steps towards this myself, but of course it is a significant undertaking.
Hi Ali, your forum posts look the same to me as everyone else’s. Is it possible for you to share a screenshot? Maybe via Dropbox or something, if you use that.
Alizter, the reason your forum posts are not “padded” is that you’ve chosen the “Text” markup option rather than the default “Markdown+Itex” option: check the radio buttons underneath the text entry box.
I see now. Thanks Mike. Here is a screenshot sorry about the ads
Thanks for catching typos!
I have now fixed all the instances that you mentioned explicitly.
For your “and in several places” I scrolled around a little and didn’t see any further instances right away. I am sure there are, and I can try to hunt them down later.
Thanks. I made the change on the page that was inserted in this one, geometry of physics – basic notions of category theory.
Thanks!
Question about “Example 1.22. (spaces seen via their algebras of functions)” (sorry, I’m just learning from this beautiful lecture notes).
I don’t quiet understand how this pattern relates to “space and quantity” duality or, to be more precise, how to derive this pattern from that duality.
The problem is that the duality is between generalized spaces and generalized quantities, i.e. adjoint pair between categories of presheaves and copresheaves on a given category of spaces, but not between the category of spaces itself and category of algebras of functions on that spaces. Is it the case mentioned in this example?
Thanks in advance!
Isbell duality here serves as an abstract guiding principle; concrete examples of space/quantity duality are (co)restrictions of the general adjunction, or sometimes not even quite that.
For that Exp. 1.22, say in the case over the site of , we want to first restrict the general presheaves over (which Isbell would consider) to those that are sheaves (the smooth sets) and the general copresheaves over (which Isbell would consider) to those that are product preserving (the smooth algebras). Then in a second step we further (co)restrict that to smooth manifolds among smooth sets, and to their ordinary function algebras among all smooth algebras.
Myself, I like to refer to Isbell duality here because to me this is the answer to an otherwise glaringly open though maybe more philosophical question. But if the mentioning of Isbell duality seems like a distraction at this point, then can just ignore it, nothing in the notes depends on it.
Thank you very much! I think I get it now.
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