Doctrines, modalities and comonads

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Mathematical Structures in Computer Science Pub Date : 2021-07-29 DOI:10.1017/S0960129521000207

Francesco Dagnino, G. Rosolini

引用次数: 7

Abstract

Abstract Doctrines are categorical structures very apt to study logics of different nature within a unified environment: the 2-category Dtn of doctrines. Modal interior operators are characterised as particular adjoints in the 2-category Dtn. We show that they can be constructed from comonads in Dtn as well as from adjunctions in it, and we compare the two constructions. Finally we show the amount of information lost in the passage from a comonad, or from an adjunction, to the modal interior operator. The basis for the present work is provided by some seminal work of John Power.

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学说、模式和共性

抽象教义是一种范畴结构，非常适合在统一的环境中研究不同性质的逻辑：教义的两类Dtn。模态内部算子被描述为2类Dtn中的特定邻接。我们证明了它们可以由Dtn中的共聚单体和其中的附加基构建，并对这两种构建进行了比较。最后，我们展示了从一个comonad或从一个附加到模态内部算子的过程中丢失的信息量。约翰·鲍尔的一些开创性工作为本工作提供了基础。

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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来源期刊

Mathematical Structures in Computer Science 工程技术-计算机：理论方法

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.