Reputation
5,218
Next privilege 10,000 Rep.
Access moderator tools
Badges
2 24 71
Impact
~178k people reached

Jan
14
comment “The Yoneda embedding reflects exactness” is a direct consequence of Yoneda?
It's perfectly clear now, thank you very much for the detailed answer. I understand your reasons to call it a special case of Yoneda lemma, in that it is an illustration of Yoneda reasoning, and it certainly has the same flavor.
Jan
14
comment “The Yoneda embedding reflects exactness” is a direct consequence of Yoneda?
Thank you very much for your help!
Jan
14
comment “The Yoneda embedding reflects exactness” is a direct consequence of Yoneda?
Thank you for your answer. But it's not clear to me how this involves the Yoneda lemma...
Jan
14
comment “The Yoneda embedding reflects exactness” is a direct consequence of Yoneda?
Yes, I understand this, it's also the proof given both by Weibel and Garrett. However, Garrett in the article linked in the OP says that this result is a special case of Yoneda lemma; but I don't see how this is so, or how the proof uses it.
Jan
13
revised “The Yoneda embedding reflects exactness” is a direct consequence of Yoneda?
added 1 characters in body
Jan
13
comment “The Yoneda embedding reflects exactness” is a direct consequence of Yoneda?
@Mariano: Ah, indeed, I didn't know that. Pity there's not an \im!
Jan
13
revised “The Yoneda embedding reflects exactness” is a direct consequence of Yoneda?
added 37 characters in body
Jan
13
comment “The Yoneda embedding reflects exactness” is a direct consequence of Yoneda?
Ah, I'm sure this is an easily answered question. I feel a bit dumb posting it. However, my extreme lack of proficiency with Yoneda and his gadgets suggests me I might not come up with a clean answer myself.
Jan
13
asked “The Yoneda embedding reflects exactness” is a direct consequence of Yoneda?
Jan
12
comment A result of flat modules that *needs* to deal with the *construction* of the tensor product?
Thanks, this is slick for sure, even if Lazard's theorem is not exactly elementary IMHO. In any case, this theorem is also in Rotman, but we didn't do it on my course, so I didn't have it in mind. See my comment on Mariano's answer for another reference.
Jan
12
comment A result of flat modules that *needs* to deal with the *construction* of the tensor product?
¡Gracias! Both you and Alex used limits, so I went to that section in the book, and ta-da, he does exactly this proof in corollary 5.35, p.248. But eh, I'm just a few days into my month-and-a-half study of homological algebra through Rotman, I'm not thinking of limits yet ;) Anyway, the question is still open for another slick proof that does not use limits!
Jan
12
comment A result of flat modules that *needs* to deal with the *construction* of the tensor product?
@Alex: No, (co)limits are a couple of chapters after this. He has covered projective and injective modules, and their elementary properties. Here's the link to Google Books, maybe you'll find it useful books.google.com.uy/… . But as I added in a recent edition, I am interested in other proofs, even if they are not as "elementary" (I know I'm abusing the word, please bear with me).
Jan
12
revised A result of flat modules that *needs* to deal with the *construction* of the tensor product?
added 2 characters in body
Jan
12
asked A result of flat modules that *needs* to deal with the *construction* of the tensor product?
Jan
11
comment Why are nets not used more in the teaching of point-set topology?
@Adam: I seem to remember that Völker Runde's A Taste of Topology was quite fond of nets. I'm sure he proved Tychonoff's theorem that way.
Jan
10
comment Can someone explain the Yoneda Lemma to an applied mathematician?
thank you. But then the interpretation in the first paragraph, albeit very pretty and succinct, is not helpful in grasping the meaning of Yoneda lemma for other functors in general, no?
Jan
8
comment Can someone explain the Yoneda Lemma to an applied mathematician?
I don't see where the given functor $\mathcal{C}\to \mathrm{Set}$ in Yoneda lemma is taken into account in your first paragraph. Could you please clarify this? Thank you.
Dec
16
comment Give an explicit embedding from $\mathbb{R}P_2$ to $\mathbb{R}^4$
Related: math.stackexchange.com/questions/40833/…
Dec
11
awarded  Nice Question
Dec
11
comment Components in the Euclidean plane?
This is very similar to what is called comb space: check this out en.wikipedia.org/wiki/Comb_space