I have several related questions:
Do there exist colimits in the category of schemes? If not, do there exist just direct limits? Do there exist limits? If not, do there exist just inverse limits? With more generality and summarizing, with which generality there exist limits and colimits in Schemes?
Then, if I have a colimit of rings, its Spec is a limit in the category of affine schemes. Is it so in the category of all schemes? If not, with which generality, that is, what kinds of colimits does Spec transform to limits?
And does Spec transform limits into colimits? If not, whith which generality, that is, what kinds of limits does Spec transform to colimits?