Reputation
Next tag badge:
399/400 score
81/80 answers
Badges
24 430 745
Newest
 Good Answer
Impact
~3.9m people reached

8m
comment What do you call the category of groups with surjections (injections)?
For the class of all groups you can take the class of all free groups, for example. But there isn't a particularly convenient way (that I know of) to truncate these to a convenient class of finite groups.
21m
comment Is there a broad map, guide or list of all or most of math's fields?
press.princeton.edu/titles/8350.html
22m
comment What do you call the category of groups with surjections (injections)?
Sure: take all finite groups, of which there are countably many. (I don't know an interesting example off the top of my head.)
1h
revised Is there a systematic way of finding the factorization over the closure of $\mathbb{Z}_2$ of $p(x) = x^{32} - x$?
added 103 characters in body
2h
answered Is there a systematic way of finding the factorization over the closure of $\mathbb{Z}_2$ of $p(x) = x^{32} - x$?
2h
comment Irreducible components of tensor product representations.
For a representation over a not-necessarily-algebraically-closed field $k$, absolutely irreducible means irreducible over $\bar{k}$. But presumably in your question you're working over $\mathbb{C}$.
3h
comment Is the hemisphere of $S^4$ the unique compact 4-dimensional manifold with $\partial K = S^3$?
No, of course not, e.g. you can take connect sum with $\mathbb{CP}^2$. What you mean by $S^n/\mathbb{Z}_2$ depends on what action of $\mathbb{Z}_2$ you have in mind; do you mean a reflection?
3h
awarded  Good Answer
4h
comment What do you call the category of groups with surjections (injections)?
You don't have to leave the ordinary category of groups to ask this question. In any case, there is no such family of groups indexed by a set, because there are groups of arbitrarily large cardinality.
18h
comment Power series function on Riemann surfaces
The power series expansion uses local coordinates. Are you familiar with that term?
20h
comment Has there ever been an application of dividing by zero?
Sure. Look up projective geometry. $\frac{1}{0}$, or just $\infty$, is a convenient name for the "point at infinity" on the projective line.
21h
comment What do you call the category of groups with surjections (injections)?
I don't know a name in use. In general doing this leaves you with a less interesting category (usually most limits and colimits will now fail to exist).
1d
comment Center of a semisimple group and irreducible representations
@Elliot: it seems the conditions being required on the weight force the representation to be close enough to faithful; did you look at the cited Lemma?
1d
answered Center of a semisimple group and irreducible representations
2d
comment Clarifying notation used in Lie groups
@Hamed: I think you are not respecting the conceptual difficulty of the question. A priori, the differential of multiplication by $g$ at a point $x \in G$ is a linear map $dg_x : T_x(G) \to T_{gx}(G)$. You need to say more about how you're extracting a 1-form from this. One option is to pick a trivialization of the tangent bundle of $G$ (e.g. by left or right multiplication), so that you can interpret $dg$ as a $\mathfrak{g}$-valued $1$-form. But you should make the choice of trivialization explicit, e.g. it really does matter whether you trivialize using left or right multiplication.
2d
comment If I and J are isomorphic ideals of a ring R, does it follow that $R/I \simeq R/J$?
Isomorphic as what? Modules?
2d
comment Compute the homology group
What do you know about a sphere with two points removed? Then try three.
2d
comment Compute the homology group
Try to deformation retract onto something smaller and easier to understand. For example, do you know how to solve the analogous questions involving 1) removing a point from $\mathbb{R}^2$ or 2) removing a single axis from $\mathbb{R}^3$?
2d
comment What should I have learnt as an undergraduate?
Of course it depends on what you want to do with that degree. Do you want to go on to graduate school? Then you should know what's in graduate school prelim exams (which is just a proxy for: you should know enough that graduate school is enough time to learn what you need to write a thesis, which is itself just a proxy for...). Do you want to do something else? Then the answer is probably totally different.
2d
comment Fundamental Group of Orientable Surface
There are a couple of ways to answer that. One involves the cup product on cohomology.