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comment Higher-dimensional category theory on objects
Moreover, you can pick out $\mathbb{Z}$ categorically as the group $G$ whose only idempotents $p: G \to G$ with respect to composition are the identity and the trivial map, and which admits more than one map $G \to H$ for any nontrivial $H$. This was discussed here: mathoverflow.net/questions/194047/…
May
18
comment A mapping from the group PSL(2,R)
@user73793 Neil is right in that this is the wrong forum for your question. Try asking it instead at mathematics.stackexchange. This site is specifically for professional mathematicians and their graduate students to ask each other questions arising in their research.
May
17
comment Idempotent relations on the unit square with closed graphs
Transitivity is $R \circ R \leq R$, density (or "interpolativeness"; see also mathoverflow.net/questions/77621/…) is $R \leq R \circ R$ (see en.wikipedia.org/wiki/Dense_order#Generalizations).
May
17
comment The classifying space of an infinite totally ordered set is contractible
@ZhenLin Yes, thanks; got it. And I expect that might have been all Mostafa meant in his first comment, although he made a statement that was more general, that directed colimits of contractible spaces are contractible. Any feeling about that?
May
17
revised Vectorisation of a category
fixed some LaTeX
May
17
comment The classifying space of an infinite totally ordered set is contractible
Emanuele, isn't this just the argument given in Neil's second paragraph?
May
17
comment The classifying space of an infinite totally ordered set is contractible
@Mostafa In an earlier comment I used the phrase "directed colimit", which I believe is pretty standard. (I thought you might have meant this. The nLab ncatlab.org/nlab/show/directed+colimit notes that "direct limit" is also sometimes used, so I guess my earlier comment was overly harsh, although I do find that "direct limit" is confusing because of the synonymous usage noted above).
May
17
comment The classifying space of an infinite totally ordered set is contractible
@Mostafa It's possible to adduce some such argument, perhaps, but it would help if you were more careful with language. "Direct limit" to me is a synonym for "colimit" and it's not true that homotopy group functors preserve all colimits (see e.g. math.stackexchange.com/questions/320812/…). Aside from that, the statement in your first comment that I was asking about was stated more generally than for spaces having the homotopy type of a CW complex, which is why I asked. (If you don't think it's true in that extra generality, that's fine.)
May
17
comment The classifying space of an infinite totally ordered set is contractible
@Mostafa Do you have a reference for the claim that a directed colimit of contractible spaces is contractible? Am I missing something obvious?
May
17
comment The classifying space of an infinite totally ordered set is contractible
So if (nonempty) $P$ merely has binary joins, the same argument as in the second paragraph shows $BP$ is contractible. This hadn't occurred to me before now.
May
15
awarded  Necromancer
May
14
comment On the natural density of almost perfect numbers
Interesting. Could you edit in a good reference for the second sentence of your answer?
May
13
revised Differential operators are coKleisli morphisms of the jet co-monad
added a tag
May
12
comment Regular epimorphisms in the category of simple undirected graphs
I'm not sure this question is trivial; the category of simple loop-free graphs (or sets equipped with symmetric irreflexive relations) is not a topos or quasi-topos and is not a particularly nice category.
May
12
comment Composition of rational functions
Re your edit: can two $i_j$ be the same?
May
4
comment Is the following conjecture equivalent to the Second Hardy-Littlewood Conjecture?
@TheMaskedAvenger Your first comment is hard for me to understand. It seems to me (on reflection) that Wojowu believed the question to be appropriate for MO, so there is (a) no reason why he would write "... and this is why this forum is the wrong one...". And (b) my point was that no one who felt that way should be answering in the first place! Perhaps what you meant to say is that reasons should always be conveyed in comments (as opposed to answers)? I don't agree. I can see a point however that the help center could be yet more explicit on topicality. Maybe you'd like to take that cause up?
May
4
comment How to prove this determinant is positive?
user23765: if you click on the share button under a question or answer, a little pop-up box will appear, and there you will see 'cite' in the lower left-hand corner. Click on that and you will see a suggested format for citation. Nice question, by the way.
May
4
comment Meaningful review of Moriwaki's “Arakelov Geometry”
I can understand why some think it's an unusual request, but I think it's fine for this question to stay open. Particularly in asking for classroom experiences: gathering and assessing a spectrum of opinion here might lead to valuable information for potential users of the text. Also, something about the fact that the OP (who's a full professor at Brown) is asking under the spotlight of MO, together with the tone of his comments, gives me confidence that he will treat and acknowledge answers with propriety, and only wishes to perform his task honorably (and intends to read the book through!).
May
3
comment Is the following conjecture equivalent to the Second Hardy-Littlewood Conjecture?
I'm sure it is welcome to the OP (and certainly you're right that PNT is overkill), and it would be welcomed by others at math.stackexchange, but the idea is not to encourage others to ask questions that are off-topic for MO by posting answers to them.
May
3
comment Is the following conjecture equivalent to the Second Hardy-Littlewood Conjecture?
MO frowns on giving answers to trivial, off-topic questions.