Re: Terminology

[Jean Benabou <jean.benabou@wanadoo.fr>]

Dear Steve,

I totally agree with you.
Let me apply  your zoological criteria to Category Theory. You begin  
with the very simple notions of category, functor and natural   
transformation. But then you start piling in subclauses such as  
categories with finite limits, or regular, or abelian, or the glorious  
toposes. For functors you refine the notion to fully faithful ones or  
those who have an adjoint, or are flat, or are fibrations. I could  
give hundreds of examples, and even a meticulous zoologist would  
say:To much is to much!
Obviously Category Theory is very bad and the very idea of putting in   
a same bag groups, topological spaces, locales, and the glorious  
toposes is a misconception.
Serious mathematicians agreed with this. You are too young to remember  
the time when these mathematicians called, with zoological  
justification, this theory :  Abstract general nonsense.

All the best,

Jean




Le 14 févr. 17 à 09:48, Steve Vickers a écrit :

> Dear Fred,
>
> A good answer, but my point was that it was a bad question.
>
> You see this once you start pressing at the details. Are seals and  
> turtles fish? No, but on your definition it depends on whether  
> flippers count as legs or not. What about sea snakes? Obviously not  
> - they're snakes, that just happen to live in the sea. But then eels  
> do seem a bit more fishy.
>
> A meticulous zoologist would start piling on the subclauses to pin  
> it down more precisely, but we know that that does not actually  
> refine our understanding of zoology. It just amplifies the  
> misconceptions underlying the original question.
>
> I'm saying the same can happen in mathematics.
>
> All the best,
>
> Steve.
>
>> On 11 Feb 2017, at 20:42, Fred E.J. Linton <fejlinton@usa.net> wrote:
>>
>> Steve, et al.,
>>
>> If you want
>>
>>> a definition of "fish", but on the understanding that it has to  
>>> include
>> whales
>>
>> let me offer: "legless marine vertebrates" :-) .
>>
>> Cheers, -- tlvp
>>
>



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