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Jan
13
revised “The Yoneda embedding reflects exactness” is a direct consequence of Yoneda?
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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
Dec
11
comment Is the axiom of universes 'harmless'?
@CarlMummert: Great! I'm looking forward to it :)
Dec
11
revised Is there a less ad hoc way to find the degree of this extension?
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Dec
11
answered Is there a less ad hoc way to find the degree of this extension?
Dec
10
comment Importance of Least Upper Bound Property of $\mathbb{R}$
The conclusion of Bolzano's theorem (intermediate value theorem) would be false if $\mathbb{R}$ weren't complete. Now think of all the times you say "since $f$ is a continuous function, negative here and then positive, it must be zero somewhere in the middle"!
Dec
10
comment Are free modules injective?
@Manos: I edited in a reference for the stated result. I recommend you learn it, it is very useful.
Dec
10
revised Are free modules injective?
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