Another terminological question...

Another terminological question...

[Jeff Egger]

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.



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Re: Another terminological question...

[Steve Lack]

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.
>
>