??can we think of an abelian category x as a meta-module of a certain meta-ringoid... ??or something... ??meta-ringoid with one object for each fp ringoid r... realized wrt the meta-module as ringoid of ringoid morphisms from r to x...

?? i guess that this is supposed to be analogous to thinking of an abelian group as a module of the ringoid of finite matrixes of integers... or something... (??hmm, something about bi-module as meta-matrix?? [note added later: ??bad level slip right here??] abelian category as meta-module of the meta-ringoid of fp bi-modules of fp ringoids... ??and then later something about meta-algebras of the meta-operad of multi-modules, analogous to algebras of the operad of tensors ...??or perhaps we should be using symmetric tensors and meta-symmetric multi-modules .... ????or something...) ... part of the point being that you could also get away with for example the morita-equivalent ringoid (not closed under direct sums) corresponding to the ring of integers... and analogously you could get away with various morita-equivalent smaller meta-ringoids, or something...

(hmm, so what about "embedding theorems" here, and their decategorification??... and/or maybe categorification...)

??according to pattern i'm vaguely imagining, something like a "symmetric monoidal abelian category" would then be a meta-algebra of a meta-operad... or something like that... ??...

??hmmm... consider the subringoid of the ringoid of fp abelian groups generated by finite limits from z ... ???.... ??hmm, i have a vague memory of recently thinking about situations where the projective modules are closed under limits... ???or maybe it was even under colimits??? no, it was more like... the subringoid of projective modules has its _own_ colimits... ??or something like that?? is this related to that?? ... ??....

some aspects of attempted analogy here that i'm very vague and maybe confused about ... ??ringoid as analog of set?? ringoid with direct sums as analog of commutative monoid or something??

can/should the meta-ringoid here be "morita-equivalent" to a one-object meta-ringoid??

??in the ringoid of abelian groups, each fg free one is an absolute colimit from the full sub-ringoid containing just z...

??in the meta-ringoid of abelian categories, is the module category of an fp ringoid some sort of "absolute 2-colimit" (or something...) of the full sub-meta-ringoid containing just the ringoid of abelian groups???

hmm, i'm vaguely imagining trying to get this to connect with something about... fg free ab gp as being in some sense "cohomologically trivial", and also module category of an fp ringoid as being in some sense "cohomologically trivial" ... ??or something?? ??does this make any sense??... module category of an fp ringoid ct module category of a commutative ring... ??...

aside from bad level slips that may have crept in here... ??some possible patterns other than "meta-module of meta-ringoid" that might or might not be more salient here... meta-[algebraic theory]?? ...cateogorified monad ... ??and so forth... ??...