6,201 reputation
1625
bio website poisson.phc.unipi.it/~mossa
location Earth
age 26
visits member for 3 years, 4 months
seen 11 hours ago

I'm math student, in particular I'm interested in algebra, geometry, topology and category theory (especially higher dimensional category theory) and its application in mathematics.


May
12
comment Ultrafilter Lemma and Dimension Theorem
@AsafKaragila Ah, ok thanks. For me the dimension theorem was the one stating the existance of a basis... guess I was wrong :)
May
12
comment Ultrafilter Lemma and Dimension Theorem
I belive there's a mistake: the dimension theorem for arbitrary vector spaces is equivalent to the axioms of choice while, as you stated above, the ultrafilter lemma is not.
May
10
comment Homotopy equivalence between $X/A$ and $X$?
Touche, my bad ... Too work and sleep make Giorgio a dull boy.
May
10
comment Homotopy equivalence between $X/A$ and $X$?
This is a very well known theorem, you can find it every book of algebraic topology, for instance in Hatcher Algebraic Topology.
May
7
answered Make ring in natural way
May
6
comment Showing that every map $f : S^2 \rightarrow S^1$ is homotopic to the trivial map
@user125103 yes your proof is correct.
May
6
answered Showing that every map $f : S^2 \rightarrow S^1$ is homotopic to the trivial map
May
5
answered What are well-defined functions?
May
4
answered Can you give me some concrete examples of magmas?
May
4
comment Natural transformation is a mono iff the components are.
@magma I see that probably I should have made clear my intent from the beginning. I've edited the answer, is it ok now?
May
4
revised Natural transformation is a mono iff the components are.
Added some specifications
May
4
comment Natural transformation is a mono iff the components are.
I wanted to emphatize the fact that is one of the two implications that require the functors to be $\mathbf{Set}$-valued, while the other holds in the generic case.
May
4
comment Natural transformation is a mono iff the components are.
@magma that's not what I meant. The first part of the proof show that one of the two implication does hold for every category $\mathbf D$ as codomain of functors, i.e. it holds also for $\mathbf {Set}$. The second part shows how the other implication holds for $\mathbf{Set}$ valued functors, indeed if I remember well this second implication doesn't hold for a generic category $\mathbf D$.
May
4
revised Natural transformation is a mono iff the components are.
Fixed a grammar error
May
3
answered Natural transformation is a mono iff the components are.
Apr
29
comment Does Gödel's Completeness Theorem still hold even if the set of variables is finite?
@MauroALLEGRANZA I agree that probably Manin assume the hypothesis of infinite set of variables. Nonetheless my observation is that the proof of completeness theorem doesn't seems requiring the infinity of the set of variables in order to be proven.
Apr
28
comment Does Gödel's Completeness Theorem still hold even if the set of variables is finite?
@Amr Following your argument: if you have to prove an $L$-formula somewhere in your proof you are gonna eliminate the $10$-th variable by an application of a generalization and a particularization (application of modus ponens to formulas of the form $\forall x A(x) \rightarrow A(t)$ for $t$ a term). My conjecture is that by replacing in your proof every occurence of the variable with the term is used in the particolarization you should still be able to have a valid proof. Anyway I could be wrong, that's why I said that I suppose that should work :)
Apr
28
answered Does Gödel's Completeness Theorem still hold even if the set of variables is finite?
Apr
17
awarded  Nice Answer
Apr
11
comment Query on a simple exercise involving representations of functors.
@Niels.Remb05 take a look to the edit and see if that solves all your doubts.