benblumsmith

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In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?

linear-algebra abstract-algebra vector-spaces category-theory dual-spaces asked Dec 30 '13 at 20:28

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38 votes

Why is the cartesian product so categorically robust?

soft-question category-theory products asked May 29 '15 at 20:04

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38 votes

Is There a Natural Way to Extend Repeated Exponentiation Beyond Integers?

real-analysis functions tetration asked Aug 10 '11 at 6:13

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37 votes

Submodule of free module over a p.i.d. is free even when the module is not finitely generated?

abstract-algebra ring-theory modules principal-ideal-domains asked Jun 25 '12 at 18:21

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31 votes

Tricky contour integral resulting from the integration of $\sin ax / (x^2+b^2)$ over the positive halfline

integration complex-analysis contour-integration asked Oct 1 '11 at 14:32

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30 votes

A function that is $L^p$ for all $p$ but is not $L^\infty$?

real-analysis measure-theory functional-analysis asked Dec 12 '11 at 3:07

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30 votes

Algebraic closure for $\mathbb{Q}$ or $\mathbb{F}_p$ without Choice?

abstract-algebra field-theory set-theory axiom-of-choice asked Feb 29 '12 at 20:41

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25 votes

$\operatorname{Ann}(M\otimes_A N)=\operatorname{Ann}M+\operatorname{Ann}N$?

commutative-algebra modules tensor-products asked Jul 11 '12 at 21:41

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25 votes

Elementary problems with group theoretic solutions

group-theory big-list teaching asked Jan 15 '12 at 19:15

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22 votes

Class group of $k[x,y,z,w]/(xy-zw)$

homework algebraic-geometry commutative-algebra asked May 2 '13 at 3:19

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benblumsmith

In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?

Why is the cartesian product so categorically robust?

Is There a Natural Way to Extend Repeated Exponentiation Beyond Integers?

Submodule of free module over a p.i.d. is free even when the module is not finitely generated?

Tricky contour integral resulting from the integration of $\sin ax / (x^2+b^2)$ over the positive halfline

A function that is $L^p$ for all $p$ but is not $L^\infty$?

Algebraic closure for $\mathbb{Q}$ or $\mathbb{F}_p$ without Choice?

$\operatorname{Ann}(M\otimes_A N)=\operatorname{Ann}M+\operatorname{Ann}N$?

Elementary problems with group theoretic solutions

Class group of $k[x,y,z,w]/(xy-zw)$