Helmut

I guess a surjection is like a finite colimit or something

is it clear why a functor "preserving surjections" is the same thing as "preserving colimits"?

@Dedalus what is the indexing category of the kernel?

with the terminal object being the kernel

what is the indexing cat for the kernel? isn't it isomorphic to the standard kernel diagram?

Since the kernel diagram is finite then, the indexing limit guy is finite?

Can someone tell me what it means for a kernel to be a finite limit? I know it is a categorical limit, but why finite?

i retract my questions @anon. i think...

$M$ is artinian, so i think this makes sense

i want to say that $M/something$ has smaller length than $M$. So $M$ is generated by two guys, $u$ and $v$. The idea I'm told to consider is that you want to find a submodule of $Ru$ which is simple, call it $Ruy$. Then considering $M/Ruy$ has length less than $M$

the point is this...

i told you they were dumb questions

right...

can $Ru$ have nontrivial submodules?

cyclic means generated by one guy

implying it's not obviously cyclic, but saying that you can at least say it has a cyclic submodule

i was looking at an argument which inducts on the length of a module. one supposes $M$ is generated by two elements, so that $M=Ru+Rv$. We want to show that $M$ is actually cyclic, generated by one guy. But the argument goes that $Ru$ has merely finite length

a cyclic module

Isn't $Ru$ cyclic by definition and thus can have no submodules?

Let $M$ a module over $R$ generated by two elements, $u$ and $v$, such that $M$ has a finite length, say $r$. It is trivial to say that $Ru$ has length 1, no?

@anon can i ask you two dumb ring/module theory questions?

M=<a,b>? M=Ra+Rb? What is more standard

is there a compact way to write that a module M is generated by two elements a and b?

I should have gotten that thank you. What a gyp.

No?

$\pm$

Not if your category is a fuzzy category

if $I$ is a compact interval are integrals of functions $f\in C(I)$ continuous functions of $f$? Is the integral a continuous operator? Does that even have meaning?

Is the space of all maps from a group to the circle compact? Is there some natural topology in which to make sense of that?

i'm the author of the local-global principle. i don't do latex

i will walk out of lectures that do not correctly attribute his name, and instead replace it with a vulgar Americanism. :snob:

i insist on Григо́рий Я́ковлевич Перельма́н for Perelman

when I'm in Old Germany I do as the Old Germans do. i haven't been there in awhile, though

it doesn't help, because i have no use for small latin letters not in the English alphabet when writing people's names

must we write chinese authors names in the original ideogram?

people who use beta for the ss annoy me

Wirestross