Continuous Monads

Q3 Computer Science

Electronic Notes in Theoretical Computer Science Pub Date : 2020-10-01 DOI:10.1016/j.entcs.2020.09.009

Ernie Manes

引用次数: 0

Abstract

Continuous monads are an axiomatic class of submonads of the double power set monad. ρ-sets are an axiomatic generalization of directed sets. The ρ-generalization of continuous lattices arises as the algebras of a continuous monad and conversely. Each ρ-continuous poset has two topologies which respectively generalize the Scott and Lawson topologies. Each ρ-contnuous lattice is compact in the canonical topology if and only if the corresponding continuous monad contains the ultrafilter monad.

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的连续单体

连续单子是双幂集单子的一种公理化的子单子。ρ集是有向集的公理推广。连续格的ρ推广是由连续单子的代数产生的，反之亦然。每个ρ-连续偏序集都有两个拓扑，分别推广了Scott和Lawson拓扑。当且仅当对应的连续单子包含超滤单子时，每个ρ-连续格在正则拓扑上是紧的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Electronic Notes in Theoretical Computer Science Computer Science-Computer Science (all)

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