Quoting dusko <dusko@kestrel.edu>:
but at the end of the day, i think, we'll all agree that the source of the unreasonable effectiveness of categorical algebra is its foundational content (although there is probably a lot of it that we dont understand yet); and the other way around. eg, if you look at grothendieck's work, he started working in algebra, and ended up developing foundational structures, because he needed them. and a lot on the "algebra" side now is built upon them. ok, then for a while it was thought that he exaggerated with foundations, and that a more direct approach "could have been in better taste" (to cite eilenberg). but maby the fermat theorem would have a more useful proof if it was developed in grothendieck style. and nowadays, there is a lot of foundational content in tannaka duality etc, in TQFT in general ...
TQFT!? It seems dusko has finally discovered the shift key on his keyboard. Alex -- Alex Simpson, LFCS, School of Informatics, Univ. of Edinburgh, UK Email: Alex.Simpson@ed.ac.uk Tel: +44 (0)131 650 5113 Web: http://homepages.inf.ed.ac.uk/als Fax: +44 (0)131 667 7209