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1. • CommentRowNumber1.
   • CommentAuthorTodd_Trimble
   • CommentTimeNov 29th 2012
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   Author: Todd_Trimble
   Format: MarkdownItexI have a vague memory that there was discussion here on the pros and cons of the terminology "locally presentable", and "presentable" as a possible replacement, but I'm having trouble finding that discussion. Can anyone help?

   I have a vague memory that there was discussion here on the pros and cons of the terminology “locally presentable”, and “presentable” as a possible replacement, but I’m having trouble finding that discussion. Can anyone help?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 30th 2012
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   Author: Urs
   Format: MarkdownItexNot sure where nForum discussion would be, but _Remark 1_ at _[[locally presentable category]]_ seems to nicely sum it up: > The _locally_ in _locally presentable category_ refers to the fact that it is the _objects_ that are presentable, not the category as such. > For instance, consider the notion of "locally finitely presentable category", def. \ref{LocallyFinitelyPresentable} below, in which the generating set $S$ consists of [[finitely presentable objects]], i.e. $\omega$-small ones. If one dropped the word "locally" then one would get the notion "[[finitely presentable category]]" which means something completely different, namely a [[finitely presentable object|finitely presentable]] ($\omega$-small) object of [[Cat]].

   Not sure where nForum discussion would be, but Remark 1 at locally presentable category seems to nicely sum it up:

   The locally in locally presentable category refers to the fact that it is the objects that are presentable, not the category as such.

   For instance, consider the notion of “locally finitely presentable category”, def. \ref{LocallyFinitelyPresentable} below, in which the generating set $S$ consists of finitely presentable objects, i.e. $\omega$-small ones. If one dropped the word “locally” then one would get the notion “finitely presentable category” which means something completely different, namely a finitely presentable ($\omega$-small) object of Cat.

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeNov 30th 2012
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   Author: Todd_Trimble
   Format: MarkdownItexThanks. I knew that's what the "locally" meant, but it seems to me there was more discussion on this, maybe here or the Cafe. But the most I could find through a search was a comment by Mike at the categories list [here](http://permalink.gmane.org/gmane.science.mathematics.categories/5849).

   Thanks. I knew that’s what the “locally” meant, but it seems to me there was more discussion on this, maybe here or the Cafe. But the most I could find through a search was a comment by Mike at the categories list here.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 30th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, I do remember that we had long discussion about it, too. There is stil an faint echo of that in the [thread "locally presentable (oo,1)-category"](http://nforum.mathforge.org/discussion/1076/locally-presentable-oo1category/?Focus=8430#Comment_8430). But I can't find the original discussion either. But I feel pretty sure that this Remark 1 sums up the mathematical content of the discussion. Apart from that one can of course always have different feelings about terminology. I'd say in this case here the problem is that the concept is way too important and too common to make it likely that people will consistently pronounce all the syllables of "locally presentable".

   Yes, I do remember that we had long discussion about it, too. There is stil an faint echo of that in the thread “locally presentable (oo,1)-category”. But I can’t find the original discussion either.

   But I feel pretty sure that this Remark 1 sums up the mathematical content of the discussion. Apart from that one can of course always have different feelings about terminology. I’d say in this case here the problem is that the concept is way too important and too common to make it likely that people will consistently pronounce all the syllables of “locally presentable”.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeNov 30th 2012
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   Author: Mike Shulman
   Format: MarkdownItex...and that someone, seeing that, decided to start calling them "presentable" rather than finding a more correct name.

   …and that someone, seeing that, decided to start calling them “presentable” rather than finding a more correct name.

6. • CommentRowNumber6.
   • CommentAuthorZhen Lin
   • CommentTimeNov 30th 2012
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   Author: Zhen Lin
   Format: MarkdownItexI want to say _compactly-generated category_, but apparently that already means something.

   I want to say compactly-generated category, but apparently that already means something.

7. • CommentRowNumber7.
   • CommentAuthorMike Shulman
   • CommentTimeNov 30th 2012
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   Author: Mike Shulman
   Format: MarkdownItex(and is also the same number of syllables as "locally presentable")

   (and is also the same number of syllables as “locally presentable”)