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.

引用

页码：4989 / 5005

页数：17

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