Abstract
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.
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