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Chapitre D'ouvrage Année : 2021

Monographs, a Category of Graph Structures

Thierry Boy de La Tour
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Does a graph necessarily have nodes? May an edge be adjacent to itself and be a self-loop? These questions arise in the study of graph structures, i.e., monadic many-sorted signatures and the corresponding algebras. A simple notion of monograph is proposed that generalizes the standard notion of directed graph and can be drawn consistently with them. It is shown that monadic many-sorted signatures can be represented by monographs, and that the corresponding algebras are isomorphic to the monographs typed by the corresponding signature monograph. Monographs therefore provide a simple unifying framework for working with monadic algebras. Their simplicity is illustrated by deducing some of their categorial properties from those of sets.
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Dates et versions

hal-03430250 , version 1 (16-11-2021)



Thierry Boy de La Tour. Monographs, a Category of Graph Structures. Recent Trends in Algebraic Development Techniques, 12669, Springer International Publishing, pp.54-74, 2021, Lecture Notes in Computer Science, ⟨10.1007/978-3-030-73785-6_4⟩. ⟨hal-03430250⟩
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