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May 17 |
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Restriction of a complex polynomial to the unit circle
[deleted the comment referred to in the OP's comment from Mar. 5, 4:37] |

May 17 |
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What is the “right” universal property of the completion of a metric space?
[deleted previous comments] |

May 17 |
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What is the “right” universal property of the completion of a metric space?
[deleted previous comments] |

May 17 |
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Practical applications of algebraic number theory?
I honestly don't know [deleted previous comment] |

May 17 |
comment |
Given a finite field $K$, what are the possible degrees of a polynomial $p\in K[x]$ such that $x\longmapsto p(x)$ is one-to-one?
There seem to be some discussion on the subject of permutation polynomials in Ch. 7 of Lidl-Niederreiter (books.google.com/…). [I hope I understood the question correctly. In the title shouldn’t $x\mapsto f(x)$ really be $c\mapsto f(c)$?] |

May 15 |
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Reference request for category theory works which quickly prove the theorem which generalises the 1st isomorphism theorem for groups/rings/…
Perhaps instead of category theory, you should look at some basic book on universal algebra, for example, you can try part 3 of Cohn’s algebra. |

May 14 |
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is the presheaf category of a locally small category locally small?
Thanks for the pointers! The link doesn't seem to work, but I will look at nLab now that I know what to look for. I suppose that at the moment (before finished reading Mac Lane) I'll stick to the foundations described in Section 1.6 of Mac Lane. Although limited (as I now see..), these foundations seem to be sufficient in Mac Lane (as Mike Shulman told me in a comment...), and I should probably not "dive" into something else right now. Thanks again for your help. |

May 14 |
comment |
is the presheaf category of a locally small category locally small?
Thank you very much! Having such tips from an expert is extremely helpful. I have a million more question to ask, but I guess these comments aren't the right place for such a mini course... |

May 14 |
comment |
is the presheaf category of a locally small category locally small?
Thank you very much for your answer! I hope it is OK that I ask another silly question: Is my comment above correct, but just useless, because (for some reason that I still don't understand) "locally small" can refer to non-small hom-sets that are in bijection with small sets? [I'm assuming a single universe, as in Mac Lane.] |

May 13 |
comment |
is the presheaf category of a locally small category locally small?
@Todd Trimble: Is this simple argument wrong? Consider a non-empty hom-set $\widehat{C}(F,G)$, and let $\tau$ be in this hom-set. If the hom-set is small, then by transitivity of the universe, $\tau$ is small too. But $\tau$ is just a function with domain $\operatorname{obj}(C)$ (so $\tau$ is a triple with $\operatorname{obj}(C)$ as its first component). But then from transitivity again we get $\operatorname{obj}(C)\in U$, a contradiction. (So, in general,the answer to the original question is ``no'') |