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Graphs, hypergraphs, and properads

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Abstract

A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad monad, first in terms of presheaves on elementary graphs, second in terms of groupoid-enriched hypergraphs.

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Acknowledgments

I thank Philip Hackney, Marcy Robertson, Donald Yau and Sophie Raynor for useful feedback, and acknowledge support from Grant number MTM2013-42293-P of Spain.

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  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

    Joachim Kock

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  1. Joachim Kock
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Kock, J. Graphs, hypergraphs, and properads. Collect. Math. 67, 155–190 (2016). https://doi.org/10.1007/s13348-015-0160-0

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  • DOI: https://doi.org/10.1007/s13348-015-0160-0

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