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Monographs, a Category of Graph Structures

Abstract : 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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https://hal.univ-grenoble-alpes.fr/hal-03430250
Contributor : Thierry Boy de la Tour Connect in order to contact the contributor
Submitted on : Tuesday, November 16, 2021 - 10:29:40 AM
Last modification on : Wednesday, July 6, 2022 - 4:20:48 AM
Long-term archiving on: : Thursday, February 17, 2022 - 6:21:35 PM

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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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