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We give an algebraic presentation of directed acyclic graph structure, introducing a symmetric monoidal equational theory whose free PROP we characterise as that of finite abstract dags with input/output interfaces.
Categorical algebra
Mac Lane, S.: · 1965
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Languages for monoidal categories
Jay, C.B.: · 1989
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On the PROP corresponding to bialgebras
Pirashvili, T.: · 2002
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Composing PROPs
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Axioms for bigraphical structure
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Temperley-Lieb algebra: from knot theory to logic and computation via quantum mechanics
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An abstract characterization of Thompson’s group F {F}
Fiore, M., Leinster, T.: · 2010
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