### Questions (22)

 3 Catalog of Categories 3 How to interpret this definition of adjoint functors? 3 How to define rigorously the category of all functors? 3 What is a positively oriented Jordan curve? 2 Prove that $\rho (\cup_{n\in\mathbb{N}}A_n)=\sum_{n\in\mathbb{N}}\rho (A_n)$

### Reputation (377)

 +10 How can I show that for all $v\in V$ there's $F\in V^{**}$ such that $F(f)=f(v)$ for all $f\in V^*$? +10 Convolution in a compact Hausdorff topological group +10 $\int _{\mathbb{T}^n}f(t)g(x-t)d\lambda (t)\in\mathbb{C}$ for all $x\in\mathbb{T}^n$ and $f,g\in L^1(\mathbb{T}^n)$? +10 Are these all the properties required to have a category?

 1 How to interpret this definition of adjoint functors? 1 Show that $a^2+b^2+c^2$ is a square when $\frac{1}{a}+\frac{1}{b} = \frac{1}{c}$ and $a,b,c\in\mathbb{Q}$ 0 What is a positively oriented Jordan curve?

### Tags (43)

 1 category-theory × 6 1 factoring 1 functors × 3 1 number-theory 1 adjoint-functors × 2 1 rational-numbers 1 contest-math 0 measure-theory × 4 1 elementary-number-theory 0 linear-algebra × 3

### Bookmarks (49)

 1360 Visually stunning math concepts which are easy to explain 335 'Obvious' theorems that are actually false 182 Teaching myself differential topology and differential geometry 88 If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable 78 Is there any easy way to understand the definition of Gaussian Curvature?