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Oct
20
answered How can function fields have different degrees over the projective line
Oct
20
comment Why is the Borel Algebra on R not equal the powerset?
And to see why it's difficult to give a completely explicit example of a set which isn't in the Borel $\sigma$-algebra, see this MO answer.
Oct
20
comment Why is the Borel Algebra on R not equal the powerset?
There are lots of subsets of $\mathbb{R}$. What makes you think that every subset of $\mathbb{R}$ can be written as a countable union of countable intersections of open and closed subsets?
Oct
19
comment Relationships between zero morphisms and least morphisms
No, I don't see any reason why bi-monotone composition should imply that the bottom morphism (assuming it even exists!) is preserved.
Oct
19
comment What is algebraic geometry?
@anon: That's one way of doing things, but that is precisely not what algebraic geometry does...
Oct
19
comment Are Indizations cocomplete
This category is more properly called the "ind-completion of $\mathcal{C}$".
Oct
19
comment How to see $\operatorname{Spec} k[x]$ for non necessarily algebraic closed field $k$?
Can you say more about why $G$ acts transitively on $S$, when $\bar{k}$ is possibly non-separable over $k$?
Oct
18
comment A question about the definition of fibre bundle
You need to use the condition $\textrm{proj}_U \circ \phi_U = \pi |_U$.
Oct
18
comment $n$-sheeted branched covering
This is not algebra but geometry – specifically complex geometry. How familiar are you with this subject?
Oct
18
comment Other ways of proving that the set of all countable ordinals is uncountable
Not Russell's paradox so much as Burali-Forti's paradox, but they're closely related.
Oct
18
comment Projective module over a ring
$R^\kappa$ for an infinite cardinal $\kappa$ is not free in general. You mean $R^{\oplus \kappa}$.
Oct
18
comment The image of the spec functor under a restriction
The dual of the category of abelian groups can be embedded in the category of locally compact abelian groups, by Pontryagin duality.
Oct
18
comment The image of the spec functor under a restriction
What's a prime ideal in a non-unital ring?
Oct
18
comment Is there a quicker, nicer way to show that the union of compact sets is not necessarily compact?
Why not take $S_n = \{ n \}$? Then $S$ is just an infinite discrete set, which is obviously not compact.
Oct
17
revised How to show that $\Delta[n]$ isn't Kan fibrant…?
edited tags
Oct
17
answered How to show that $\Delta[n]$ isn't Kan fibrant…?
Oct
17
revised What is a copresheaf on a “precategory”?
added 484 characters in body
Oct
17
comment Pushout not a homotopy invariant
Indeed, a very similar example works: there's a cospan $1 \rightarrow I \leftarrow 1$ whose pullback is empty, but contracting $I$ to a point first makes the pullback $1$ instead.
Oct
17
comment How do you encode a programm in a category?
You can encode programs as numbers, and you can encode numbers as sets, and you can encode sets as categories, so yes, technically, you can encode programs as categories. This is totally unhelpful, however.
Oct
17
comment Algebraic Varieties, field extensions and tensor product
OK, but what is the definition of $X_K$? Or for that matter, $X \otimes_k K$?