Algebraic cocompleteness and finitary functors

摘要

A number of categories is presented that are algebraically complete andcocomplete, i.e., every endofunctor has an initial algebra and a terminalcoalgebra. For all finitary (and, more generally, all precontinuous) setfunctors the initial algebra and terminal coalgebra are proved to carry acanonical partial order with the same ideal CPO-completion. And they also bothcarry a canonical ultrametric with the same Cauchy completion.