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.
G. Markowsky, "Categories of Chain-Complete Posets," Theoretical Computer Science, vol. 4, no. 2, pp. 125-135, Elsevier, Dec 1977.
The definitive version is available at http://dx.doi.org/10.1016/0304-3975(77)90031-7
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