ON THE GREATEST FIXED-POINT OF A SET FUNCTOR

被引：37

作者：

ADAMEK, J ^{[1
]}

KOUBEK, V ^{[1
]}

机构：

[1] CHARLES UNIV,FAC MATH & PHYS,PRAGUE 1,CZECH REPUBLIC

来源：

THEORETICAL COMPUTER SCIENCE | 1995年 / 150卷 / 01期

关键词：

D O I：

10.1016/0304-3975(95)00011-K

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The greatest fixed point of a set functor is proved to be (a) a metric completion and (b) a CPO-completion of finite iterations. For each (possibly infinitary) signature Sigma the terminal C-coalgebra is thus proved to be the coalgebra of all C-labelled trees; this is the completion of the set of all such trees of finite depth. A set functor is presented which has a fixed point but does not have a greatest fixed point. A sufficient condition for the existence of a greatest fixed point is proved: the existence of two fixed points of successor cardinalities.

引用

页码：57 / 75

页数：19

共 15 条

[1] LEAST FIXED-POINT OF A FUNCTOR [J].

ADAMEK, J ;

KOUBEK, V .

JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 1979, 19 (02) :163-178

[2]

Adamek J., 1974, COMMENT MATH U CAROL, V15, P589

[3]

Adamek J., 1990, AUTOMATA ALGEBRAS CA

[4]

ADAMEK J, 1977, LECTURE NOTES COMP S, P199

[5]

ARNOLD A, 1980, FUND INFORM, V4, P445

[6] COMPLETIONS OF PARTIALLY ORDERED SETS [J].

BANASCHEWSKI, B ;

NELSON, E .

SIAM JOURNAL ON COMPUTING, 1982, 11 (03) :521-528

[7] TERMINAL COALGEBRAS IN WELL-FOUNDED SET-THEORY [J].

BARR, M .

THEORETICAL COMPUTER SCIENCE, 1993, 114 (02) :299-315

[8]

KOUBEK V, 1971, COMMENT MATH U CAROL, V12, P175

[9]

Koubek V., 1979, J PURE APPL ALGEBRA, V14, P195

[10] A FIXPOINT THEOREM FOR COMPLETE CATEGORIES [J].

LAMBEK, J .

MATHEMATISCHE ZEITSCHRIFT, 1968, 103 (02) :151-&

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