余递归代数、余递归单子与Bloom单子
Corecursive Algebras, Corecursive Monads and Bloom Monads
摘要：
一个代数称为余递归的，如果从每一个余代数中存在唯一的余代数到代数的同态.我们证明了自由余递归代数可以作为终结余代数（看作一个代数）和自由代数的余积而得到.证明了自由上递归代数的单子是自由上递归单子，其中上递归单子的概念是Elgot迭代单子的推广，类似于上递归代数推广完全迭代代数.我们还刻画了自由余递归单子的Eilenberg-Moore代数，称之为Bloom代数。
英文摘要：
An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and free algebras. The monad of free corecursive algebras is proved to be the free corecursive monad, where the concept of corecursive monad is a generalization of Elgot's iterative monads, analogous to corecursive algebras generalizing completely iterative algebras. We also characterize the Eilenberg-Moore algebras for the free corecursive monad and call them Bloom algebras.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
