4,141 reputation
21647
bio website bruno.stonek.com
location Montevideo, Uruguay
age 25
visits member for 3 years, 10 months
seen 4 hours ago

Math student in Université Paris 13.


Jun
25
comment Reference request: is mathematics discovered or created?
@Pete: it is not a research paper what I have to write (if I understand well what you mean by "research paper"), just a 10-15 pages survey on some topic of interest. To be honest, the course is not on philosophy of science but rather on "university, science and society". Some of the early lectures were on the history of science and some epistemology; based on that I want to write something related to that part of the course, and not the more socially-oriented part which is not of great interest to me. In fact, I've matriculated to this course only because it is compulsory and there is no...
Jun
25
comment Reference request: is mathematics discovered or created?
@user6312: thank you. Also, lol @ "Bruce"!
Jun
25
comment Reference request: is mathematics discovered or created?
I fixed your link. I know of this article and have read it before (and liked it a lot). It is of course related. Thank you.
Jun
25
revised Reference request: is mathematics discovered or created?
fixed link & spelling
Jun
25
asked Reference request: is mathematics discovered or created?
Jun
22
comment Reference for Algebraic Geometry
@Mariano: Oh yes, that's true, I had forgotten about that one. It's the one a teacher here recently taught a course with (sadly I couldn't take it) on the subject, and when I leafed through it it looked quite wonderful.
Jun
22
answered Reference for Algebraic Geometry
Jun
18
comment if $s \implies \lnot w$, does $\lnot s \implies w$?
If it is sunny, it doesn't rain. But if it doesn't rain, it doesn't mean it has to be sunny. --Edit: ah, I hadn't seen Didier's answer below ;P
Jun
15
comment Why is an empty function considered a function?
...so, the initial element in Set (--see en.wikipedia.org/wiki/Initial_and_terminal_objects)
Jun
15
comment Equivalent conditions for a preabelian category to be abelian
@Theo: Sorry, I hadn't had time to finish checking the argument. I did now, it's perfect. Thank you once again, you've been of huge help!
Jun
15
accepted Equivalent conditions for a preabelian category to be abelian
Jun
14
comment Equivalent conditions for a preabelian category to be abelian
@Theo: If I understand correctly, since $e=coker(f)$ and $y$ is another map such that $yf=0$, then there exists a unique $y'$, by definition of cokernel, no? I don't see how it is needed to use again that $e$ is epi.
Jun
14
comment Equivalent conditions for a preabelian category to be abelian
@Theo: Thanks! I'm digesting your answer. I don't understand this part, though: "Since e is epi, this factorization is unique and hence e is a cokernel of k."
Jun
14
comment Equivalent conditions for a preabelian category to be abelian
@Theo: again, thank you very much. I'm absorbing your previous comment right now. I don't quite get your "on the other hand", it seems you're using that $g$ is a retraction, but that isn't necessarily so. In any case, dually you get a right inverse, and existence of right and left inverse implies iso. Also, you're using that if f is epi then it's the cokernel of its kernel: I didn't know that (I think that's what Freyd proves on 2.11... "Ker and Cok are inverse functions", come on...)
Jun
14
comment Equivalent conditions for a preabelian category to be abelian
@Theo: I still can't do it. The answer seems to be hidden in Freyd's book, which I find quite unreadable. I put it aside and tried to prove that $\overline{f}$ is mono-epi, so this would prove that it is iso. I couldn't do it, and in fact, I'm also unable to prove that in an abelian category mono-epi implies iso. What a failure! I wonder whether it is true, in fact, that mono implies section and epi implies retraction?
Jun
12
comment Equivalent conditions for a preabelian category to be abelian
@Theo: I see. Combining Freyd's theorems 2.12, 2.18 and 2.18* with Mac Lane's CWM proposition 1 in page 195 (the analogue of Freyd's "unique factorization"), I believe I can write a tidy proof. I shan't do so today, though. Thank you for your assistance.
Jun
12
comment Equivalent conditions for a preabelian category to be abelian
@Theo: Thank you, I'm aware that product and coproduct coincide with biproduct. I shall take a look at Freyd; I already had, but I didn't recognize it under that name and (to my taste) awkward wording.
Jun
12
comment Equivalent conditions for a preabelian category to be abelian
@Theo: would you consider posting an answer? Thank you very much.
Jun
12
comment Equivalent conditions for a preabelian category to be abelian
@Theo: I'm having difficulties proving that $\overline{f}$ is mono, anyway. I'm trying to prove that $Ker(\overline{f})=0$ by using the universal property of ker, but I'm not seeing how every other map $X\to Coim(f)$ factors through zero...
Jun
12
comment Equivalent conditions for a preabelian category to be abelian
@Theo: I'm trying. But is it true in an abelian category that mono-epi is iso?