TERMINAL COALGEBRAS IN WELL-FOUNDED SET-THEORY
TERMINAL COALGEBRAS IN WELL-FOUNDED SET-THEORY
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DOI：
10.1016/0304-3975(93)90076-6
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发表时间：
1993-06-21
影响因子：
1.1
通讯作者：
BARR, M
中科院分区：
文献类型：
--
作者：
BARR, M
本文表明，为了获得Aczel和Mendler关于集合范畴上函子的终代数存在性的定理，完全没有必要深入研究非良基集合论这样的奇特事物。此外，我们讨论了从集合上函子的初始代数到终端余代数的规范映射，并表明在许多情况下，它将前者作为后者的稠密子集嵌入到某种自然拓扑中。举例来说，我们计算各种简单内函子的末端余代数。
This paper shows that, in order to obtain the theorem of Aczel and Mendler on the existence of terminal coalgebras for an endofunctor on the category of sets, it is entirely unnecessary to delve into such exotica as non-well-founded set theory. In addition, we discuss the canonical map from the initial algebra for an endofunctor on sets to the terminal coalgebra and show that in many cases it embeds the former as a dense subset of the latter in a certain natural topology. By way of example, we calculate the terminal coalgebra for various simple endofunctors.