bio | website | maths.ed.ac.uk/~tl |
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visits | member for | 4 years, 6 months |
seen | 13 hours ago | |
stats | profile views | 6,244 |
Apr 17 |
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Universal property of module categories over monads
@Dimitri: I think Martin means the category of algebras, which some people call the category of modules. |
Apr 14 |
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How to minimize $-\sum p_b \ln{p_b}$?
Not sure this is really the stuff of MathOverflow rather than math.stackexchange, but thanks for giving the link. |
Apr 14 |
answered | How to minimize $-\sum p_b \ln{p_b}$? |
Apr 3 |
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a naive question about the second dual of a vector space
Yes, that's the paper I had in mind. I was really thinking of a simpler version of Proposition 5.4 (concerning just endofunctors, not monads). Double dualization is a codensity monad, i.e. a right Kan extension of a certain kind, and so has a certain universal property. This implies that it's terminal in the sense I mentioned. But there must surely be a more direct proof of this, and maybe it would be possible to adapt it to answer your actual question. |
Apr 2 |
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a naive question about the second dual of a vector space
Interesting question. I know there is a unique endomorphism of the functor $V \mapsto V^{**}$ that restricts to the identity on finite-dimensional vector spaces. (More generally, $(\ )^{**}$ is terminal among all endofunctors of Vect that restrict to the identity on FDVect.) This is similar in spirit to your question, and I was hoping to use it to answer your question, but I haven't managed. |
Apr 1 |
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What keeps asymptotic Goldbach's conjecture out of reach of current technology?
To state the obvious, one possible reason is that it's false... |
Mar 26 |
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What is a cograph of an n-functor?
Yes, that's exactly what it is. |
Mar 20 |
reviewed | Approve suggested edit on Fractional Derivatives Of Sums |
Mar 20 |
reviewed | Approve suggested edit on Fractional Derivative of A specific function |
Mar 20 |
reviewed | Approve suggested edit on Finding the Fractional Derivative of This Function |
Mar 19 |
awarded | Good Answer |
Mar 11 |
awarded | Nice Answer |
Mar 10 |
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Sources of Theorem drafts by the original author
@AlexDegtyarev: do people really discriminate against proofs based around clear geometric ideas? Or is it more that "intuitively clear" geometric ideas are not so easy to turn into watertight proofs? |
Mar 5 |
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The proof of Belyi theorem by Lando and Zvonkin
Welcome, Paz, and please don't apologize for asking a specific question. We like specific questions here! (Whether anyone's expert enough to answer it is another matter.) |
Mar 4 |
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Entropy in elimination theory, or a brief remark by Gelfand-Kapranov-Zelevinsky
The following certainly isn't an answer to your question, but I thought a bit about some related things a while ago; maybe there's some connection between discriminants and entropy via geometric invariants such as mixed volume. See here, especially Mark Meckes's pointer to Richard Gardner's article. |
Mar 4 |
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Entropy in elimination theory, or a brief remark by Gelfand-Kapranov-Zelevinsky
Thanks. The link didn't work for me ("you've reached your page viewing limit" or some such), but when I searched for it myself, I found it. Google, eh. |
Mar 4 |
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Entropy in elimination theory, or a brief remark by Gelfand-Kapranov-Zelevinsky
For those of us intrigued by your question but without the book to hand, could you explain a bit more of the context? Thanks. |
Jan 24 |
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Why the term “monad” in homological algebra?
OK, I think user42369 has answered my question. |
Jan 23 |
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Why the term “monad” in homological algebra?
That's informative, but I'm still puzzled. I can see that monads in category theory have something "single" about them (just as monoids do). But how does a three-term complex with certain properties have a feeling of "singleness" about it? |
Jan 21 |
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Why the term “monad” in homological algebra?
I don't know why they're called that, but the Wikipedia article you link to dates this usage to 1964, whereas I'm pretty sure the category theory usage was coined later than that (late 1960s, I guess). You weren't asking this, but I might as well add: in category theory, the word "monad" is intentionally like "monoid", since from an appropriately elevated viewpoint, monads and monoids are the same thing. |