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Oct
13
answered Why determinant is a natural transformation?
Oct
13
answered What is lattice with arbitrary suprema called?
Oct
12
comment Do free monads on $Set^I$ (functor category) always exist?
Only $\mathcal{C} = \emptyset$ would do that.
Oct
12
revised Do free monads on $Set^I$ (functor category) always exist?
added 505 characters in body
Oct
12
answered Do free monads on $Set^I$ (functor category) always exist?
Oct
11
comment Question about the definition of a category
The homotopy category is known to be non-concrete and has multiple morphisms between objects.
Oct
10
comment A nice example of a functor naturally ismorphic to Stone-functor.
Hmmm... I would have thought the early motivating examples were in homology and homotopy, rather than general topology...
Oct
9
comment Affine space over non algebraically closed field
@QiaochuYuan: $\mathbb{A}^n / k$ is probably not too bad. It also reminds the reader that this is a scheme over $\operatorname{Spec} k$, which is important if you want the set of $k$-points to be precisely $\mathbb{A}^n (k)$!
Oct
9
comment Affine space over non algebraically closed field
Hartshorne writes $\mathbb{A}^n_k$ for the scheme. I forget where I picked up the notation $X(k)$ for $k$-points of $X$.
Oct
9
comment Affine space over non algebraically closed field
In standard notation, isn't $\mathbb{A}^n (k)$ the set of $k$-points in $\mathbb{A}^n$, i.e. the set of homomorphisms $\mathbb{Z}[x_1, \ldots, x_n] \to k$? Perhaps it would be better to talk about the scheme $\mathbb{A}^n_k$.
Oct
7
comment prove that it's not provable
If something is provable then it is true in all models. $\mathbb{Q}$ is a model of the theory of fields and does not have $\sqrt{2}$, so the existence of $\sqrt{2}$ cannot be proved.
Oct
5
answered Why the morphisms of vector spaces, over different fields is not interesting?
Oct
5
comment Splitting Exact Sequences
You don't even need concreteness or elements here – a completely morphism-theoretic proof is possible and isn't awkward in the least.
Oct
5
comment Why the morphisms of vector spaces, over different fields is not interesting?
It's not exactly the same – you have first choose an embedding of $\mathbb{R}$ into $\mathbb{C}$, and there might be more than one.
Oct
4
comment How to prove that monos are injective?
Sorry, I was thinking of the right cancellation property and surjectivity, which has to be phrased in just the right way to avoid assuming the law of excluded middle.
Oct
4
comment How to prove that monos are injective?
Double bonus point: Prove this without using the law of excluded middle!
Oct
4
answered Localization at an element is intersection of localizations at primes not containing the element
Oct
3
revised Tensor product of monoids and arbitrary algebraic structures
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Oct
3
comment Tensor product of monoids and arbitrary algebraic structures
Yes, I see the problem now. Hmmm. I'll have to think about this more...
Oct
2
answered Tensor product of monoids and arbitrary algebraic structures