There are several comments I could make to this posting, but I will confine myself to two. First, I was around all through the 70s (and most of the 60s) and I have no idea what categorists did to earn the opprobrium described below. A colleague of mine commented one day maybe 25 years ago, that it seemed in the 60s that category theory would be important, but it hasn't turned out that way. I am not sure what didn't turn out that way, but that seemed to have been the general opinion. Second, a couple of papers by Linton and Manes in the Zurich Triples Book (LNM #80) makes very explicit the connection between triples and universal algebraic theories. Although doubtless out of print, a dozen of us put a lot of effort into retyping it in tex and republishing it as a TAC reprint. If someone wants to go ahead and replace every instance of "triple" by "monad" go ahead. Also Beck's tripleableness theorem is in Beck's thesis, another TAC reprint also retyped by volunteers. Incidentally (although Paul is well aware of this) every paper of mine later than 1985 and every earlier paper of which I had an electronic trace, is available on my personal ftp site. Also incidentally my wife and I retyped Grothendieck's Tohoku paper and are waiting only for proof-reading by the Van Osdols to post it (hint, hint, since I know Don reads this group). Michael On Thu, 10 Dec 2009, Paul Taylor wrote:
I'm not too sure what the context was, but Andre' Joyal said on 7 December,
Category theory is a powerful mathematical language. It is extremely good for organising, unifying and suggesting new directions of research.
I completely agree.
It is probably the most important mathematical developpement of the 20th century.
It is too early to tell.
[Comment attributed to Zhou Enlai (Chinese Communist leader 1949-76) when asked his opinion of the French Revolution.]
But we cant say that publically.
I think we should be wary of slapping ourselves on the back too much.
The fact is that category theory alienated the rest of the mathematical world. Since the damage had been done in the 1970s, well before my time, I have never managed to work out how this happenned, or who was responsible.
Probably it was the result of haughty claims about being the "most important mathematical development", and about being the foundations of mathematics before any serious technical work was done to justify this. Of course the ignorance and arrogance of mathematicians outside our subject had a lot to do with it too.
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