The Topos Of A Connectivity Space
St\'ephane Dugowson (Quartz)
TL;DR
This paper introduces a topos construction associated with each connectivity space, providing a new categorical perspective on connectivity structures.
Contribution
It defines a topos for connectivity spaces, offering a novel categorical framework for analyzing connectivity properties.
Findings
Establishes the existence of a topos for each connectivity space
Provides a new categorical approach to connectivity
Lays groundwork for further topological and categorical studies
Abstract
In this short note, a topos - called the topos of the connectivity space - is associated with every such space.
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Taxonomy
TopicsDistributed systems and fault tolerance · Computability, Logic, AI Algorithms · Optimization and Search Problems