903 reputation
411
bio website
location Oslo, Norway
age 26
visits member for 4 years
seen Jun 22 at 12:03

Master student in algebraic topology at the University of Oslo.


May
25
comment Is there a universal property of $\text{Spec}(-)$?
I clarified this assumption in the OP.
May
25
comment Is there a universal property of $\text{Spec}(-)$?
I knew about that, but I'm thinking about $\text{Spec}$ as a functor $\text{Ring}^{op}\to\text{LRSpaces}$. This question may still be silly though :)
Apr
28
comment Natural Isomorphism $\mbox{Hom}(\oplus_\alpha A_\alpha,G) \simeq \prod_\alpha \mbox{Hom}(A_\alpha,G)$
@Qwirk: That's precicely what happens in this case as well, but with different words in it. By definition, a morphism from the coproduct is the same thing as a morphism from each of its factors.
Apr
25
comment What is a natural isomorphism?
Nice meta-observations :)
Apr
25
comment A question on differentiability of the inverse of strictly monotonically increasing functions
Yup, the answers down below cover it. Just to be sure you're not missing out on anything; the inverse $f^{-1}$ of a real to real function can aquired from the graph of $f$ by just flipping the xy plane along the diagonal. If you haven't already you might find it worthwhile to connect the algebraic picture below with this geometric picture.
Apr
9
comment How to “grok all the major pieces” of math
+1 for category theory.
Apr
9
comment How can there be alternatives for the foundations of mathematics?
Interesting! I've been hoping you could get around it somehow.
Apr
9
comment How can there be alternatives for the foundations of mathematics?
You talking about the appendix which I removed? Sheaf topoi are Grothendieck topoi. I'm not entirely sure how this all ties together. But it's a huge and interesting field no less.
Apr
7
comment Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$
Oh gee of course! :p
Apr
7
comment Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$
Bravo, bravo! I quite like it. I want to read about "because the equality holds for infinitely many values of x (and we are working over Z...)". Do you have a reference? It's probably in my algebra book, and it does make sense.
Apr
6
comment Same symbol “$\partial$” - different things ( the boundary $\partial A$ / partial derivative $\frac{\partial f}{\partial x}$)?
The integral $\int_a^b f(x) dx$ of a map $f:[a,b]\to\mathbb{R}$ is the same thing as the difference $F(b)-F(a)$ where $F$ is the antiderivative of $f$. Notice that $a,b$ are the boundary points of $[a,b]$, and that $f=F'$. This connection between integration over a cell and its boundary gives us Stokes' theorem. When integration happens in several dimensions, we need the partial derivatives in there. I'm not sure about if this choice of notation was intentional.
Apr
3
comment Is it ever true that $\Omega^n(\bigvee_I X)\simeq\bigvee_I\Omega^n X$?
@Ryan Sounds good to me. Thank you!
Apr
3
comment Two definitions of exactness
Thanks a lot! I suspected it would have something to do with building the limit from products and equalizers. That fact will probably prove a good exercise :)
Mar
24
comment Is it ever true that $\Omega^n(\bigvee_I X)\simeq\bigvee_I\Omega^n X$?
Yeah I noticed that one too. If there is such a homotopy-equivalence ever (unless $X$ is $n$-connected or something) it seems to be highly non-obvious. I've not read that, no. Do you have a good reference for it? Thanks!
Mar
24
comment Is it ever true that $\Omega^n(\bigvee_I X)\simeq\bigvee_I\Omega^n X$?
I would think so. $\Omega X:=\hom_*(S^1,X)$ and $\Omega^n X:=\hom_*(S^1,\Omega^{n-1}(X)$ is the $n$-th loopspace of pointed maps. Was that what you were thinking about?
Mar
24
comment Is it ever true that $\Omega^n(\bigvee_I X)\simeq\bigvee_I\Omega^n X$?
Depending on the response I might ask this on MathOverflow as well. Please stop me with a comment if you think this question is too broad for that page :D