Yes, I certainly agree that the notions you mention are probably quite well=known for people working in some areas of category theory.

See: locally presentable category in nLab and they also have a tag on MO, accessible category in nLab, Accessible category in Wikipedia and they also have a tag on MO.

I haven't heard of pure morphism before.

The question is whether some of them are too specif (perhaps pure-morphism).

@ArnaudD. I agree with your assessment both of accessible-categories and locally-presentable-categories. (But I do not feel strongly enough to recreate the latter again. And I do not plan to removed (accessible-categories).)

We will see what other users think. (Certainly we all not the only users who check which new tags were created.

This shows a slight advantage of suggesting a new tag on meta first - there is at least a chance that somebody who knows the topic will comment on the tag and say whether they consider it useful. (Also I will certainly admit that most tag-related discussions in the tag management thread, including proposal for new tags, go largely unnoticed.)

Some people have stronger feelings about the question whether new tags should be on meta first: Should every new tag be discussed on meta before creation?

To get back to these specific tags (from category theory), simply the fact that a corresponding exists on MathOverflow is for me argument which sways me at least a bit in direction of keeping the tag.

Perhaps it should be also added that if some user creates one or two new tags with every question they post, that is very likely not an optimal approach to creating tags.

It seems like we agree on all these matters. Like you, I'm not sure I'd recreate locally-presentable-categories, but I thought I would say something "for the record", in case someone thinks the tag is not useful and removes it.

Yes. I'd guess that if a tag is created and removed several times (generalization was mentioned recently), then it will eventually lead to a discussion on meta bout the tag.

So we will see what happens with the tag you mentioned.

As far as I can tell, this was the first time the tags named locally-presentable-categories or accessible-categories were created.

@MartinSleziak Out of curiosity, do you try to post a message here for every new tag? Because a couple weeks ago I noticed a question with a new tag, but I don't think I've seen you post anything here.

@ArnaudD. Yes, I do but it is natural that I occasionally miss something.

I do not know whether this could be automated in some way.

And it is questionable whether or not something like this might be useful - but at least when removal of some tag is suggested on meta, quite often it's possible to find in this room when the tag was created.

But it is certainly better to make a post about a new tag than just post here some dummy post just in order to prevent the room from getting frozen.

@ArnaudD. Well, I found no post with such tags among deleted questions, either: data.stackexchange.com/math/query/883845/… data.stackexchange.com/math/query/883845/…

Of course, I cannot claim that those SEDE queries are 100% reliable.

Some case when tag would not be shown in revision history was if it was at some point merged by a moderator into another tag. Or burnination has similar effect - it is as if tag never existed.

Although for these tags burnination is very unlikely, and I doubt that they were merged into some bigger tag at some point.

Yes, burnination would be very surprising here.

(In case you're curious : the new tag that I mentioned a few comments above was "ends-coends", and the creator removed it after I suggested replacing it with limits-colimits.)

I see. It was here: math.stackexchange.com/posts/2981684/revisions And we can use this as a test of the query I mentioned above: data.stackexchange.com/math/query/927958/…

I should say that it is basically just a modification of arjafi's query posted in this meta discussion: Can you tell who created a tag.

Coends and adjunctions: "I was reading Fosco Loregian's paper This is the co/end, my only co/friend, and here's something that I don't understand in an exercise."

Nice title for a paper.