Martin Brandenburg
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84/100 score
 Sep 29 awarded Notable Question Sep 17 awarded Good Question Sep 16 comment How should one think about sheafification and the difference between a sheaf and a presheaf Thank you. I've edited it. Sep 16 revised How should one think about sheafification and the difference between a sheaf and a presheaf deleted 1 character in body Sep 16 revised A characterization for the ideals of $A+XB[X]$ and $A+XB[[X]]$ added 224 characters in body Sep 16 answered A characterization for the ideals of $A+XB[X]$ and $A+XB[[X]]$ Sep 13 comment What are the worst notations, in your opinion ? I agree with Todd Trimble. Also, notice that there is no notion of "two sets are disjoint" for a category theorist. It only makes sense to say that two arrows $A \to X \leftarrow B$ are disjoint. Sep 13 comment What are the worst notations, in your opinion ? I agree with Qiaochu Yuan here. Also, $\mathbb{Z}/n$ can be seen as a cyclic group with a chosen generator. Sep 13 comment What are the worst notations, in your opinion ? Why not writing $f^{\circ 2} = f \circ f$ and $f^{\circ -1}$? And $f^2$, $f^{-1}$ are defined pointwise as usual. Sep 13 comment What are the worst notations, in your opinion ? @darijgrinberg: OK, what about $\mathbb{F}(q)$? Sep 13 comment What are the worst notations, in your opinion ? Recently I have written a survey article on $2$-categories (in german, though) and have found that the usual rule of composition is confusing as hell. I chose $f \ast g$ to denote the composition "first $f$, then $g$", and everything looks fine now. I don't like the notation $f;g$. Sep 13 comment What are the worst notations, in your opinion ? By the way, many people use $(a,b)$ for the gcd of $a$ and $b$. Now that is confusing ... Sep 13 comment $A$ is isomorphic to $A \oplus \mathbb{Z}^2$, but not to $A \oplus \mathbb{Z}$ I suspect that all short proofs or counterexamples are flawed. There are already three deleted answers, and Richard Stanley's suggestion above does not work, unfortunately. +1 for Eric Wofsey's comment because it makes visible the standard error with these types of questions which is otherwise hidden (to most MO users) in the deleted answers. I am almost sure that there are abelian groups $A$ with $A \cong A \oplus \mathbb{Z}^2$ and $A \not\cong A \oplus \mathbb{Z}$, but the construction will be probably quite intricate. Sep 12 awarded Good Question Sep 12 reviewed Approve $A$ is isomorphic to $A \oplus \mathbb{Z}^2$, but not to $A \oplus \mathbb{Z}$ Sep 12 awarded Nice Question Sep 12 asked $A$ is isomorphic to $A \oplus \mathbb{Z}^2$, but not to $A \oplus \mathbb{Z}$ Sep 10 awarded Good Answer Sep 8 comment Analogy between the exterior power and the power set @Dan Petersen: Thank you for your interest. I will write it up, but I cannot promise that this happens soon. Aug 23 awarded Nice Question