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May
19
answered Tensor product of a vector space and a field
May
19
revised What's the significance of defining group as a group object in category $\mathcal{Set}$?
added stuff
May
19
answered What's the significance of defining group as a group object in category $\mathcal{Set}$?
May
16
answered Quotient modules isomorphic $ \Rightarrow$ submodules isomorphic
May
14
answered Doubt about Yoneda Embedding as image of the hom functor
May
13
answered question about $p$-Sylow subgroups
May
13
revised Unit for Left Adjoint to the Inclusion Functor
Fixed some typos (functor $i$ cannot be composed with object of the category $\mathbf{Set}/I$)
May
13
answered Clarification about the definition of term algebras
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.