?? so consider inclusion morphism between cocones that's not a localization .... ????geometric interpretation ???? ... ???? ..... vs that of localization as "toric zariski-open (reverse ...) inclusion" .... ????....

?? for example x and xy as generators of subring of k[x,y] ?? .... ????....

??? formal colimits wrt localizations vs formal colimits wrt more general morphisms here (??? ...) .... ???? .... ??? some semi-systematic non-trivial way of thinking of former as special case of latter .... ???? ....... ???? ..... "planar graph theorem" ... ??? ..... ??? maybe ... ???property of diagram, less restrictive than requiring all arrows to be realized as localizations, but still sufficient to yield theory of "combined doctrine" ... ???? .....