A Guided Tour in the Topos of Graphs
Sebastiano Vigna
TL;DR
This paper surveys the presheaf topos of graphs, demonstrating that transition graphs of nondeterministic automata form separated presheaves under the double negation topology, and showing their category is a quasitopos.
Contribution
It provides a detailed analysis of the topos-theoretic structure of graphs and automata, revealing new categorical properties and connections.
Findings
Transition graphs are separated presheaves for the double negation topology.
The category of transition graphs forms a quasitopos.
The paper offers a comprehensive topos-theoretic perspective on graphs and automata.
Abstract
In this paper we survey the fundamental constructions of a presheaf topos in the case of the elementary topos of graphs. We prove that the transition graphs of nondeterministic automata (a.k.a. labelled transition systems) are the separated presheaves for the double negation topology, and obtain as an application that their category is a quasitopos.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Formal Methods in Verification