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Yes. "Coöperate" is nuts to me because the second o represents a perfectly normal English sound and a hyphen would work fine, if anything is needed at all. The broader point is that people and institutions love to make absolutist pronouncements about correct usage but they are rarely justified, and often only make things more effortful or jarring to the reader. DJing is easier to read than "D.J.-ing" is my point.
Isn't that's an En dash you've put there?
Ha! Now fixed!
(It should always be 'En dashes' and 'Em dashes'.)
Why? It has always been lowercase 'em' and 'en' in British English usage, used to signify the measurement of the type block 'N' and 'M'. Written as 'en' and 'em' to avoid confusion among printers between discussions about type measure and about actual letters. US or International English may differ idk.
Why not, if you're professionally concerned with them (as I guess you are)?
I don't know. There are just various ways of separating non-diphthong vowels. A trema to my mind should only be used for different vowels, e.g. Haïti. Another problem with it is that it has different functions in different languages, e.g. in German it's *not* separate from the letters A, O, and U in Ä, Ö, and Ü—these are whole letters, or "Umlaute"—the diaresis is not the Umlaut/'umlaut', that's the whole letter. The hyphen in co-operate etc. is therefore a much better option. (I generally think that for most English compound nouns, which in English are generally not drawn together, hyphens are the preferred way of indicating the unity of the noun. Exceptions apply, but for clarity I think that's the best way.)
I haven't read too many, but found plenty to disagree with in every single one I've seen. It's a terribly confused situation in German since the ridiculous spelling 'reform', which has left generations adrift.
Isn't that's an En dash you've put there?
Why not, if you're professionally concerned with them (as I guess you are)? (It should always be 'En dashes' and 'Em dashes'.)