On coalgebras over algebras

被引：7
作者：
Balan, A. [1 ]
Kurz, A. [2 ]
机构：
[1] Univ Politehn Bucuresti, Dept Math 2, Bucharest, Romania
[2] Univ Leicester, Dept Comp Sci, Leicester LE1 7RH, Leics, England
来源：
THEORETICAL COMPUTER SCIENCE | 2011年 / 412卷 / 38期
基金：
英国工程与自然科学研究理事会;
关键词：
Coalgebras; Algebras over a monad; FINAL COALGEBRAS; EQUATIONS; CATEGORY; AUTOMATA;
D O I：
10.1016/j.tcs.2011.03.021
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We extend Barr's well-known characterization of the final coalgebra of a Set-endofunctor H as the completion of its initial algebra to the Eilenberg-Moore category Alg(M) of algebras associated to a Set-monad M, if H can be lifted to Alg(M). As further analysis, we introduce the notion of a commuting pair of endofunctors (T, H) with respect to a monad M and show that under reasonable assumptions, the final H-coalgebra can be obtained as the completion of the free M-algebra on the initial T-algebra. (C) 2011 Elsevier B.V. All rights reserved.
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页码：4989 / 5005
页数：17
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