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Martin Sleziak
Martin Sleziak
10:32 AM
The main reason why I suggested synonym (rather than retagging) the tag etcs is that people who are interested in that area (foundations, categories) are probly used to the shortcut ETCS and they might object if the tag disappears completely.
But maybe I am too cautions.
The questions which currently have the etcs tag are:
6
Q: How do we compare models of ETCS?

David RobertsThe elementary theory of the category of sets (nLab) gives axioms on a category such that it is a category of sets. In answering this MO question I realised that we might have trouble comparing different models of ETCS. So here are some questions starting with easy ones (which I should know the a...

ct.category-theory set-theory etcs lo.logic
2
Q: Can we define geometric morphisms (between ETCS categories) elementarily?

David RobertsThe ETCS axioms give conditions on a category for it to be a category of sets. These axioms can be written out in first order language, resulting in a finite axiomatisation of the category of sets. Given a model of ZFC one can form the associated category of sets and this will satisfy the axioms....

ct.category-theory etcs set-theory lo.logic
26
Q: Who needs Replacement anyway?

David RobertsThe set theory ETCS famously comes without the Replacement axiom schema (or an equivalent) that is part of ZFC. One (to me, not apparently useful) set that one cannot build in ETCS is $\coprod_{n\in \mathbb{N}} P^n(\mathbb{N})$. Jacob Lurie pointed out on Michael Harris' blog1 the example of taki...

ct.category-theory lo.logic set-theory foundations etcs
5
Q: Is ETCS well-founded?

mattecapuI can't find a statement about the axiom of regularity anywhere in treatments of ETCS. Perhaps this is due to the unfortunate clash of terminology with 'foundations'.

set-theory foundations etcs
10
Q: Categorial foundations via "categories of algebras"

Dean YoungThere are categorical foundations for mathematics axiomatizing the category of sets (Lawvere's ETCS), cartesian closed categories (type theory), and the category of spaces (homotopy type theory). Categories in foundations commonly have properties such as distributivity of products over coproducts...

ct.category-theory foundations etcs
19
Q: Could groups be used instead of sets as a foundation of mathematics?

Oscar CunninghamSets are the only fundamental objects in the theory $\sf ZFC$. But we can use $\sf ZFC$ as a foundation for all of mathematics by encoding the various other objects we care about in terms of sets. The idea is that every statement that mathematicians care about is equivalent to some question about...

ct.category-theory set-theory lo.logic foundations etcs
The tag-excerpt was created by quid.
yesterday, by YCor
I guess the tag etcs should be replaced with the name 'elementary-theory-category-of-sets] (34 characters). There are 6 occurrences, it can be done manually. It's in coherence with avoiding abbreviations in tags. Most people unrelated to this topic have no idea of the meaning of ETCS.
@DavidRoberts You had some activity in this tag. (I am not sure whether you also created the tag, but you have asked some of the questions in that tag.) What do you think about renaming etcs as suggested above?
And since I have pinged you, I will mention also diffeology - which you created recently. I will just remind that the tags which have only a single question are automatically removed after 6 months, unless they have a tag-wiki.
 
 
2 hours later…
YCor
YCor
1:03 PM
@MartinSleziak It seems that a natural feature-request on meta would be that whenever somebody types something as a search for tags (either looking for tags, or writing a tag in a new question), the tags for which the typed word appears in the tag excerpt/info (and not only in the tag name itself) would be listed.
 
Martin Sleziak
Martin Sleziak
1:28 PM
It is interesting idea, however, I am not not sure to which extent this would really work.
One problematic thing is that some commonly used words might hide tags which contain this word as a part of the name.
Another thing is that quite often tag-excerpts contain something like: "Do not use this tag for xyz, in such cases use the (abc) tag instead." This feature would show those tags, too. (I.e., if I entered some word in the tag field, I would be shown also the tags which are explicitly discouraged for that purpose.)
Anyway, if/when you have time (and if you still think that it is a good idea), you can try that feature request on the local meta or on Meta Stack Exchange.
 
 
3 hours later…
YCor
YCor
4:50 PM
@MartinSleziak I clearly have the idea of first sorting those tag with the given word (as now listed) and then those where it appears in the tag excerpt/info.
The problem with "do not use this tag for..." already exists with the current sorting. For instance if you're interested in algebra, the tag "abstract-algebra" is proposed. If you're interested as lattices (ordered sets), the tag "lattices" is proposed.
 
Martin Sleziak
Martin Sleziak
5:11 PM
BTW I will mention although this - which is a bit related: Should MathOverflow request suggested tags feature?
As far as i can tell, this already exists - and it can be switched on sites which request that.
However, the suggestion got score 2 (+3/-1) here on MO. So it seems that the local community does not consider it as a good idea.
 
 
6 hours later…
David Roberts
David Roberts
11:10 PM
@MartinSleziak I'm not completely opposed, though it is a standard term in foundations. There are plenty of things in mathematics that are completely opaque to outsiders (like, what on earth is an expander graph? An end extension? Is it related to the end(s) of a manifold?) so I'm not super keen to change it. You'll notice that in my posts I give a tiny explanation of what ETCS is, so that is just part of asking a good question.
At the very least we should have a tag synonym, so that someone who searches for ETCS, knowing what it is, doesn't come up blank.
 

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