Prince M

As someone who has been on and off with alcohol in my lifetime, people like that are so annoying.

ok no problem

Does that make sense? I feel like I worded that poorly. Basically take the thing you want to be a functor and use it to define the category so that the "functor" is a functor. Or would that route be poorly behaved

@AlessandroCodenotti could we also perhaps be perverse and just define the functor $F$ that yields a sheaf of $A$-modules, and then just define the essential image to be a category where we only specify the maps $F(i)$ where $i$ was a morphism in $OP(X)$.

ok, cool that is the kind of answer I am looking for.

" a sheaf of O-modules or simply an O-module over a ringed space"

Like, each module is a module over a different ring

Quick question, something I never realized. If A is a sheaf of rings, and F is a sheaf of A-modules, what category does F take values in?

Haha it was actually a really cool class. It was the lead in to Sobolev spaces

I told this man he was off his rocker and weak derivatives were nonsense

I somehow got roped into this crazy analysis class once and the proff tried to teach us about functions that were $\pi$ times differentiable

hard no

no

My parents are in PS right now

@Ultradark I am pretty amateur in algebraic geometry, I am just reaching modern AG

Definitely not the highest spot, more like the lowest spot

yeah I am downtown Seattle

I am in Washington and would prefer it stop snowing

While passing time throughout the snow blizzard

I am just trying to fit in

wait I thought it was common for sub-par aspiring algebraic geometers to make snide remarks about things just because they don't have any background, but play it off like the things aren't cool enough

Theres a snow blizzard where I live I am stuck inside here listening you all talk about science particle

Well this conversation looks boring. No offense. Sounds science-y

I am not sure how that site works though, so maybe thats normal.

Does anyone know if nLab was heavily edited within the last year? I am looking at some pages I read maybe 4 - 8 months ago and they all seem different.

Thanks @MatheinBoulomenos

Immediately we see a_1 must be +/- 2, but the choice of -2 contradicts the fact that f(0) > 0, so the only solution is the one you found

Composing f with itself yields f(f(x)) = a_0(1+a_1)+a_1^2x

@silent you get immediately that degree of f is at most 1 so f can be written in the form f = a_o + a_1x

It seems to make sense because the thing remaining to check would be that the inclusion composed with F is naturally isomorphic to the identity functor on C’, but that would just be the restriction of the identity functor on C? So essentially I would be checking that F restricted to C’ and identity restricted to C’ are naturally isomorphic but doesn’t that follow from the fact that they were naturally isomorphic over C

If I have a category C and a subcategory C’ and I define a functor F: C —> C’ and I show that F composed with the inclusion functor i: C’ —> C is naturally isomorphic to the identity functor on C, is that enough to conclude and equivalence of categories between C and C’

I’m pretty perverse most of the time it probably just looks like me

most of the names that seem to suggest some physical or visual interpretation make sense to me in some way, but I couldn’t picture what a flabby sheaf should look like

I like that answer

So what’s flasque about a flasque sheaf!

Can anyone give me the quick and dirty on what is flabby about a flabby sheaf?

Even though it technically is, the other ring being the field of fractions, but we dont talk about A being integrally closed with respect to some ring B

I got the vibe that they mean it is not "with respect to some other ring"

Does anyone have an idea what is meant by "without qualification"?

Comin' in guns hot with a question: In Atiyah - Macdonald they say "An integral domain is said to be integrally closed (without qualification) if....."

Im working out of atiyah macdonald, they define it by universal property

I have always just accepted that it would be the case otherwise the property would be useless... but I tried to come up with an easy justification of why it would be true and I actually dont really have anything

Amateur hour question over here: Can anyone give me the spark notes proof of why if two modules are isomorphic, if one is flat so is the other?

I guess I'll just do what I should do... and try to prove it : 0

No problem :) thank you for that information!

this is probably a no brainer but I have 0 topology background

Sorry for coming in guns hot with a question, but I dont feel like its worthy of a post on MSE - are minimal primes preserved through a homeomorphism of spectrum?

In my experience, there are times when figuring out the answer to extreme hypothetical questions can save the person from having to ask 10x as many questions about realistic scenarios, because the answers follow from the extreme cases

I am not a regular user on “MoneySE”, but I don’t see why this question seems ill received just because the scenario is so improbable. I like the question, not because I’m learning about “what to do in the case no transactions taking place for a stock” but because the hypothetical scenario is helping the OP (and me) make sure we know exactly what causes a stock price to fluctuate. If you’re going to build an investment strategy with the goal of making Money and making money directly depends on the fluctuations of stock prices - knowing the mechanics of the fluctuations seems like a good idea