Recently, the following tag synonyms were created by a MathOveflow moderator: abstract-algebra $\to$ ra.rings-and-algebras, geometry $\to$ mg.metric-geometry and discrete-mathematics $\to$ co.combinatorics. You can see the new synonyms in the list of tag synonyms (Wayback Machine). The three tags (abstract-algebra), (geometry) and (discrete-mathematics) were deprecated, you can find links to their original tag-excerpts here: What is the correct way to handle questions with deprecated tags? There is also some related discussion in MO editor's lounge. (Possibly you can just check the starred messages if you want to get a brief overview without reading the whole things.)
As far as I can tell, the tags weren't merged when the synonyms were created.1 This has the advantage that creation of the synonym can be reversed. (If the tags are merged and synonymized, even after canceling the synonym the question will still have the new tag and there isn't a way to restore the original tags.) If you check some older questions which originally had those tags, you can still see there (abstract-algebra), (discrete-mathematics) or (geometry). IIRC the tags will remain in this way until the question is edited.
The fact that the tags are now synonyms means that:
- When somebody tries to add the old tag, it is automatically replaced by the new tag. (The same thing happens if a question is edited.)
- The old tags behave in search as their synonym. (For example, if you click on geometry, you are shown the posts tagged mg.metric-geometry.)
Of course, creating the synonym means that some questions do not have appropriate tags. (For example, not every question which was tagged (geometry) is a good fit for (mg.metric-geometry).) However, as the questions still display the original tag, at least we can recognize the "suspect" questions while viewing the question.
It seems that the synonyms were created without discussion here on meta. (I do no know whether the moderators discussed this step among them.) The purpose of this question is to get some input from MathOverflow community on these synonyms. (Since this influenced tags on approximately 700 to 750 questions, that seem to be quite significant change, the MathOverflow community probably should be aware that this happened.)
Main question. Should these synonyms remain, or should they be cancelled? Should the tags be merged or not? (And if they are merged, should the deprecated tags be removed or should they remain as a synonym?) If currently merging is not suitable, should they be merged later? Should the tags be blacklisted - to prevent users from adding them to new questions?
The moderator who created the tag synonyms mentioned two aspects as advantages of the current state: "I see two advantages to the current situation with the synonyms: (1) No new uses of the old tag, and automatic retagging on edit. (2) We can still search out the tag by hand (e.g., using a browser's "find" function on a page full of mg.metric-geometry questions) and manually change them over time."
Preventing new questions from using the deprecated tags. It is true, that with these synonyms in place the deprecated tags are not added to new questions, as they are automatically changed to other tags. One thing to consider is whether this might lead to incorrectly tagged question. (Some people might not noticed that when they entered (geometry), it was converted to (mg.metric-geometry).)
If we want to prevent the tags from being added to new questions, the tags could be blacklisted instead of having a synonyms. This is what I proposed before: The existing deprecated tags should be blacklisted.
Changing tags without bumping. Synonyms have changed which tags are found, for example, when searching for (mg.metric-geometry). (Even the ones which were originally tagged (geometry).) This was done without having to bump any questions. There are also other tools available to mods which can achieve such large-scale changes. For example, if the tag (geometry) is manually cleaned in such way that all questions in this tag fit into (mg.metric-geometry), then the two tags can be merged. (This replaces all instances of one tag by the other one.) Or if the tag (geometry) is in the state where all existing questions would be correctly tagged after omitting this tag, moderators can ask Stack Exchange staff to burninate the tag (which removes all instance of the tag completely). However, both burnination and merging should IMO be done only after the sufficient clean-up of the tag.
Finding the questions with deprecated tags. As mentioned above, after this change some questions are not tagged correctly and could possibly require further clean-up. However, it is now more difficult to find those posts. (For instance, searching for posts tagged (geometry) now returns the posts with the (mg.metric-geometry) tag.) The deprecated tags on those questions are still visible, but they are more difficult to find. (They would be easier to find if the tag synonyms were canceled. As mentioned above, we can still prevent the deprecated tags from being added to new questions using blacklisting.)
It is possible to use various SEDE queries to search among the questions which have the deprecated tags. For example, this query returns the questions which have the given tag.2 And you can add various further criteria to the query.3 (Although it is definitely less comfortable than searching directly on the site. Moreover, the data in SEDE are only updated once a week.)
In case it is useful, users who are interested in the tag management could create some list of questions which had the deprecated tags (either on site or off site). I have made a post to show what I mean here: Recent tag synonyms for deprecated tags. (The post is visible to 10k+ users and mods. I deleted the question after posting it - I did not want to have two closely related posts on meta after each other. Moreover, if the linked question will be actually used, it could probably get bumped a lot.)
Since not everybody is familiar with tag-related actions, let me also briefly summarize some terminology.
- Tag synonym. A synonym (tag1) $\to$ (tag2) means that the tag (tag1) will be automatically replaced by (tag2) when added to question or when editing a question. And in many other aspects, (tag1) now behaves as (tag2). (For example, searching for (tag1) gives the posts with (tag2).) See also the FAQ post: What are tag synonyms and merged tags? How do they work?
- Merging two tags. Merging should be used carefully, since it is not a reversible process. If a tag (geometry) is merged into (mg.metric-geometry), that means that all instances of (geometry) are changed to (mg.metric-geometry). (Without bumping any questions.) The change is also made in the revision history. (So from the question it will no longer be visible which tag it had before merging.) There is a section "What are merged tags?" in the FAQ post: What are tag synonyms and merged tags? How do they work?
- Blacklisting a tag. Blacklisting prevents the tag from being added to new questions. (And, at the same time, if some question already has the blacklisted tag, it must be changed when the question is edited - an edit which still keeps the blacklisted tag cannot be saved.) I tried to explain the details concerning blacklisting in my previous post: The existing deprecated tags should be blacklisted. There is also a FAQ post: What is a blacklisted tag?
- Burnination means that all occurrences of the tag are removed from all questions which have the given tag. Again this is done without bumping any questions. Unlike merging, this cannot be done by mods, so a member of Stack Exchange staff has to be involved. See also: What does it mean to “burninate” a tag?
1See also: What is the difference between merging two tags and synonymizing two tags? and What is the difference between a synonym and merging a tag?
2In SEDE you can see the status when the database was last updated, which was before creating the synonym. (It is updated once a week.) As far as I can tell, the questions will be still visible in the SEDE queries even after the next update of SEDE. (Unless the moderators also merge the tags.) You can check some similar instances - the tags which were made synonyms without merging - on Mathematics, such as span or conditional-probability. (Here are related discussions on Mathematics Meta: Unable to add “span” tag to (linear algebra) question and Cannot add tag “conditional-probability”.)
3 Examples of various queries can be found in chat: https://chat.stackexchange.com/transcript/10243/2020/5/5 https://chat.stackexchange.com/transcript/10243/2020/5/6