Dear all, In ``basic concepts of enriched category theory'', Kelly writes:
Since the cone-type limits have no special position of dominancein the general case, we go so far as to call weighted limits simply ``limits'', where confusion seems unlikely.
My question is this: why does he not apply the same principle to the concept of powers? Instead, he introduces the word ``cotensor'', apparently in order to reserve the word ``power'' for that special case which could sensibly be called ``discrete power''. [This leads to the unfortunate scenario that a ``cotensor'' is a sort of limit, while dually a ``tensor'' is a sort of colimit.] Is there perhaps some genuinely mathematical objection to calling cotensors powers (and tensors copowers) which I may have overlooked? Cheers, Jeff. P.S. I specify ``genuinely mathematical'' because I know that some people are opposed to any change of terminology for any reason whatsoever. Obviously, I disagree; in particular, I don't see that minor terminological schisms such as monad/triple (even compact/rigid/autonomous) are in any way detrimental to the subject. I also disagree with the notion (symptomatic of the curiously feudal mentality which seems to permeate the mathematical community) that prestigious mathematicians have more right to set terminology than the rest of us. I see no correlation between mathematical talent and good terminology; nor do I understand that a great mathematician can be ``dishonoured'' by anything less than strict adherence to their terminology---or notation, for that matter. __________________________________________________________________ Looking for the perfect gift? Give the gift of Flickr! http://www.flickr.com/gift/