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added at Grothendieck universe at References a pointer to the proof that these are sets of -small sets for inaccessible . (also at inaccessible cardinal)
The entry lax morphism classifier was started two yeats ago, is actually empty!
I have created lax morphism, with general definitions and a list of examples. It would be great to have more examples.
Added related concepts section with links to coherent category, coherent hyperdoctrine, Pos, and Frm
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Added table of contents and links to geometric category and geometric hyperdoctrine
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I have added some things to frame. Mostly duplicating things said elsewhere (at locale and at (0,1)-topos), but I need these statements to be at frame itself.
At overt space there was a remark that since the definition quantifies over “spaces”, the overtness of a single space might depend on the general meaning chosen for “space”, but that no example was known to the author. I added an example involving synthetic topology, which may not be quite what the author of that remark was thinking of, but which I think is interesting.
I incorporated some of my spiel from the blog into the page type theory.
There has GOT to be a better photograph than that! Is there anyone here in Oxford? Can they go and get a picture for us?
the table didn’t have the basic examples, such as Gelfand duality and Milnor’s exercise. Added now.
I made some very minor changes to the introduction at descent. I hesitate to do more but at present the discussion does not seem that readable to me. Can someone look at it to see what they think? The intro seems to plunge in deep very quickly and so the ‘idea’ of descent as that of gluing local information together, does not come across to me. The article is lso quite long and perhaps needs splitting up a bit.
Added some content to display map from Taylor’s book. Not very deep, mostly as a reference to the respective section for me.
I added to category of elements an argument for why preserves colimits.
Created basic outline with some important connections. Yang-Mills measure, after all the main concept which makes this special case interesting, and references will be added later.
Edit: Crosslinked D=2 Yang-Mills theory on related pages: D=2 QCD, D=4 Yang-Mills theory, D=5 Yang-Mills theory.
(Today’s arXiv) A homotopification
and few more additions.
I added the HoTT introduction rule for ’the’, then added a speculative remark on why say things like
The Duck-billed Platypus is a primitive mammal that lives in Australia.
tried to bring the entry Lie group a bit into shape: added plenty of sections and cross links to other nLab material. But there is still much that deserves to be done.
Created:
An internal category object in the category of smooth manifolds in which the source and target maps are submersions.
Sometimes, the smooth manifold of morphisms is allowed to have a boundary, in which case the restrictions of the source and target maps to the boundary are required to be submersions themselves.
i have split off (copied over) the paragraph on the first uncountable ordinal from countable ordinal to first uncountable ordinal, just in order to make it possible to link to “first uncountable ordinal” more directly. Cross-linked with long line.
brief category:people-entry for hyperlinking references at skyrmion, atomic nucleus
I tried to brush-up the References at period a little.
I have trouble downloading the first one, which is
My system keeps telling me that the pdf behind this link is broken. Can anyone see it? (It may well just be my system misbehaving, wouldn’t be the first time…).
at decidable proposition I found the simple basic idea a bit too deeply hidden in the text. In an attempt to improve on this I have added right before the subsections of the Idea-section this quick preview:
External decidability: either or may be deduced in the metalanguage;
Internal decidability: may be deduced, hence “ or not ” holds in the object language.
Okay?
Recorded at subsingleton that a different nomenclature also exists, in which “subterminal” and “subsingleton” are not synonymous (see for instance Anders Kock in page 2 of Algebras for the Partial Map Classifier Monad).
an entry for mere proposition had been missing. Created a minimum, just so as to satisfy links.
moving the following ancient query box out of the entry:
+– {: .query} What about the ’or’ of parental threat? Consider the logician parent who says “Come here or I’ll smack you” to his child and smacks even after obedience as they believe in the inclusive ’or’. -David
That's no different from ’If you don't come here, then I'll smack you.’, which also suggests (but does not state) the converse. And in fact, no parent, logician or otherwise, is actually making the promise implied by the clause; if the child comes to such a parent and then kicks the parent in the shin, then the parent will still smack the child. Instead, if you want to make that promise, then you say ’If you come here, then I won't smack you.’ explicitly. This has a very different tenor (unless you say it in a wink-nudge mafia kind of way), as it's a promise rather than a threat. (I know, it's only a promise, which is still different in tenor than a statement that is both promise and threat, as an exclusive disjunction would be. But I still hold that your statement is only a threat.) Note that a logician child who believes the parent's literal expression would still choose to come if avoiding smacking is the highest priority; but the reason is that refusal guarantees a smack, not that obedience necessarily avoids it. That is why the wise child also throws in a contrite expression and an oral apology, to improve the odds. —Toby
I see there’s a literature on the subject including “The Myth of the Exclusive ’Or’” (Mind, 80 (317), 116–121). —David
Also: I argued above that the meaning of ’Come here or I'll smack you’ must be weaker than exclusive disjunction, since the parent will smack the child anyway under some circumstances. However, I agree that it is stronger than inclusive disjunction, but that is because we may go beyond the literal meaning of the words and apply a Gricean implicature. To be specific, if the parent intends to smack the child regardless, then the parent should say ’I'll smack you’ by the Maxim of Quantity, but the parent in fact said something more wordy. Thus we conclude that the parent does not intend to smack the child if the child comes, without ruling out the possibility that the parent will still smack the child for some other reason, as yet unanticipated. —Toby =–