6,136 reputation
1623
bio website poisson.phc.unipi.it/~mossa
location Earth
age 26
visits member for 3 years, 2 months
seen Aug 6 at 12:58

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.


Oct
15
comment Steve Awodey “Category Theory” - possible error
@porton Since $i^{-1}(U')=\{x \in A \mid i(x)=x \in U'\}=U' \cap A=U$, so $f^{-1}(U')=(i \circ \bar f)^{-1}(U')=\bar f^{-1}(i^{-1}(U'))=\bar f^{-1}(U)$.
Oct
15
comment Steve Awodey “Category Theory” - possible error
@porton My apologize, I've added some details I hope now I've made myself more clear. If that's not the case feel free to ask.:)
Oct
15
revised Steve Awodey “Category Theory” - possible error
added some details
Oct
14
comment Steve Awodey “Category Theory” - possible error
@porton no it's not in Awodey's book, it's mine :)
Oct
14
answered Steve Awodey “Category Theory” - possible error
Oct
14
comment About Equalizer in different categories
@QEUO Ok, now I've made a change that should address the last part of the question :)
Oct
14
revised About Equalizer in different categories
Adressed the second part of question
Oct
14
answered About Equalizer in different categories
Oct
13
comment Long exact sequence for cohomology with compact supports
That was my doubt since I known that compact support co-homology lives in the category of CW-complex and proper maps I was wondering how could work the constuction. Thanks @GrigoryM :)
Oct
10
comment Long exact sequence for cohomology with compact supports
Are you sure of the direction of the mapping? The embedding $i \colon U \hookrightarrow X$ shoud give a mapping $C^\bullet_C(X) \to C^\bullet_C(U)$, with direction reversed.
Oct
10
comment Structure of maximal ideals of the quotient $\mathbb{C}[x,y,z]/ I$
@Sandra Sure: for every point $p \in \mathbb A_K^n$ the ideal $I(p)=\langle x_1 - p_1,\dots,x_n - p_n\rangle$, where by $p_i$ I mean the $i$-th coordinate of $P$. This determinate the generator in $K[x_1,\dots,x_n]$ and so you can apply this result in the case $K= \mathbb C$. Then passes the generators to quotient.
Oct
10
answered Retraction and deformation of P2
Oct
10
answered Structure of maximal ideals of the quotient $\mathbb{C}[x,y,z]/ I$
Oct
10
comment Understanding cohomology with compact support
@Craig here's Hatcher book, I very good book to start learning some algebraic topology math.cornell.edu/~hatcher/AT/ATpage.html on page 251 (if I'm not mistaken) you can find a part about co-homology with compact support.
Oct
10
comment Understanding cohomology with compact support
No it doesn't depend on the choice of the compact, it must just exists a compact subset of $X$ out which vanishes in the sense said above. :) Anyway I've edited the answer again.
Oct
10
revised Understanding cohomology with compact support
made some correction
Oct
10
revised Understanding cohomology with compact support
improved answer
Oct
10
comment Understanding cohomology with compact support
Yes, that's correct: I've just noted that there was a little mistake anywayI'm gonna add some details. So stay tuned.
Oct
10
revised Understanding cohomology with compact support
made a correction
Oct
10
comment Understanding cohomology with compact support
Yes is correct. Just one remark clearly the requirement is that it must be a compact $K$ such that the cochain vanishes outside that compact, and this compact can be different for any compactly supported cochain.