Categories of chain-complete posets

We investigate the existence of various limits and colimits in three categories: CPI (chain-complete posets and isotone maps); CPC (chain-complete posets and chain-continuous maps); CPC* (chain-complete posets and chain-continuous maps). Among other things we show CPC to be complete and cocomplete. By way of contrast we show that LC* (complete lattices and chain-*continuous maps) is neither complete nor cocomplete. We also introduce a construction which yields the chain-completion of a poset and other "completions" as special cases. © 1977.