bio | website | maths.ed.ac.uk/~tl |
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visits | member for | 5 years, 2 months |
seen | Dec 23 at 4:00 | |
stats | profile views | 6,925 |
Dec 2 |
awarded | Notable Question |
Dec 1 |
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History of integral notation for coends
Do you know how we came to write the end variable at the bottom of the integral sign and the coend variable at the top? |
Dec 1 |
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What theorem constructs an initial object for this category? (Formerly “Integrability by abstract nonsense”)
@IanMorris Thanks for pointing out the dead link. I still haven't got round to publishing it, but meanwhile I've proved some further results: maths.ed.ac.uk/~tl/cambridge_ct14 and golem.ph.utexas.edu/category/2014/07/… |
Nov 30 |
awarded | Nice Answer |
Nov 27 |
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Realizing a monoid as $\mathrm{End}(G)$ for some graph $G$
To add some info on Adam's remarks: for Adámek and Rosický, a graph is a set endowed with a binary relation and a homomorphism is a function preserving the binary relation. More concretely put, their graphs are directed, can have loops but cannot have multiple edges, and may be infinite. They give that definition on p.10. The section on embedding into graphs, which presumably contains the results Adam mentions, is section 2.G. |
Nov 27 |
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a question about connected open sets in $R^2$
Oh, oops. I misread it. |
Nov 27 |
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a question about connected open sets in $R^2$
Surely the answer is an easy "no". Just take $U$ and $V$ to be disjoint. Am I missing something? |
Nov 27 |
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Realizing a monoid as $\mathrm{End}(G)$ for some graph $G$
Do you want to be specific about what you mean by "graph", or are you leaving it open-ended? |
Nov 20 |
awarded | Nice Answer |
Nov 9 |
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What measurable quantity can constrain the number of odors human can discriminate?
I'm dismayed at the votes to close and Stefan's critique. Yoav carefully explained the issues in such a way that a mathematician with no knowledge of this biological system could make a meaningful contribution. If we close this question, we might as well put a banner on the front page saying "applied math questions not welcome here". |
Oct 24 |
answered | Topological characterization of injective metric spaces |
Oct 23 |
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Characterize the category of rings
@Paul Yes! That was why I assumed that I wasn't really answering Chris's question. As you say, it's kind of a tautological statement. |
Oct 23 |
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Characterize the category of rings
OK: the category of rings together with its forgetful functor to $\mathbf{Set}$ is terminal among all categories $C$ equipped with a functor $U: C \to \mathbf{Set}$ and a ring structure on the object $U \in [C, \mathbf{Set}]$! That's probably not the kind of thing you want, though... |
Oct 23 |
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Characterize the category of rings
Do you definitely want to characterize the category of rings, rather than the category of rings together with its forgetful functor to Set? Not that I know how to do either, but I think the two questions are significantly different in character. |
Oct 22 |
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Finitely co/continuous monad induced by an operad
Another little observation: if $T$ is a finitary monad on Set (such as the one induced by an operad) and the forgetful functor from $T$-algebras to Set preserves colimits, then $T$ is of the form $M \times -$ for some monoid $M$. That doesn't quite fit your situation, but begins to suggest that there aren't any nontrivial examples. (It's Lemma 1.2 of Peter Johnstone's paper "When is a variety a topos?") |
Oct 22 |
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Finitely co/continuous monad induced by an operad
Still commenting rather than answering because I haven't got anything nontrivial to say... but if you view a monoid $M$ as an operad (with no operations of arity $\neq 1$) then the resulting monad is $M \otimes -$, which preserves colimits if your monoidal category is closed. But that's all I can think of. |
Oct 22 |
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Finitely co/continuous monad induced by an operad
Preservation of terminal objects seems like a tall order, at least when the monoidal category is cartesian. If the operad is called $P$ then this would give $\sum_n P_n = \hat{T}(1) = 1$. But maybe you're not interested in the cartesian case. If not, could you give a hint as to what kind of example you are interested in? |
Oct 17 |
awarded | Yearling |
Oct 16 |
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About the hypothesis of Zorn's lemma
Can one of the voters-to-close explain why they're voting to close? |
Oct 16 |
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How short can we state the Axiom of Choice?
@FrodeBjørdal: this is set-theoretic! Although Paul used the word "topos", $X$, $Y$ and $Z$ are sets for your purposes. It might not be the kind of set theory you want to think about, but it's set theory all the same. |