?? intuitively weird for "classical" AG morphism to fail to preserve kernels ?? ... so let's try looking at nice simple example ... ???

vector space with operator ... ??taking kernel of operator ??? ...

??already confusion here ... ??? this as tensoring with something, so left adjoint ?? ... ... ??? but "kernel" sounds right adjoint-ish ... ????? ..... ???? ... ????? ...

ok, blecchh, this is some weird mental glitch of mine ... happened the other day too, though i forget exactly who i was talking to at the time ... (?baez? ... something about "eigenspace" ...) anyway, i should have said cokernel in the first place .... ???? ...

???so we're thinking about "formal limits of quasicoherent sheaves" (?? ...) and seeing what they evaluate out to in domain vs in codomain ... ??? in part to try to figure out whether there's something "special" about how they evaluate out in the domain ..... ????? ......

so ... specific example ... of kernel (or maybe mono??) not preserved by taking cokernels ... ???

x >-> y

???we want x to have an element x1 which is not in the image of the operator ... ??and we want y to have an extra element y1 whose sole purpose is to make x1 in the image after all ... ??so it sounds like we want our mono to be a 1-by-1 matrix whose entry is the generator representing the operator .... ?????....

so then .... can we flesh this out to a clear statement about how formal limits evaluate out in the domain, and then try to come up with some sort of "geometric interpretation" of it ???? .... ?????.....

??well so for one thing, plain old generic number has now acquired property of ... ???being monic ???? ..... ????.....

???moreover, adding any (??...) constant (??? ...) to it still gives a monic .... ????......

hmmmm.... ??? "spectrum of operator" ... ????? ..... ??? ....