Re: Another terminological question...

[Steve Lack <s.lack@uws.edu.au>]

Dear Jeff,

I had a chat about this with a couple of other long-time users of the
terms tensor and cotensor (Ross Street and Dominic Verity). We
all think that, given the current overburdening of the word tensor,
this would be a sensible change.

Regards,

Steve Lack.


On 12/09/08 7:56 PM, "Jeff Egger" <jeffegger@yahoo.ca> wrote:

> 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.
>
>