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

翻译：列出了若干代数完整和共同完整的类别,即每个末端都有一个初始代数和终端煤数。对于所有有鳍的(更一般而言,所有先前后的)设定真菌体,初始代数和终端煤数被证明带有同一种理想的CPO完成率的罐头部分顺序。它们都带有同一种孔径的超度度。