Graphs, hypergraphs, and properads

Batanin, M., Berger, C.: Homotopy theory for algebras over polynomial monads. Preprint, arXiv:1305.0086 Berge, C.: Hypergraphs, vol. 45 of North-Holland Mathematical Library. North-Holland Publishing Co., Amsterdam (1989) Berger, C.: A cellular nerve for higher categories. Adv. Math. 169, 118–175 (2002) Berger, C., Melliès, P.-A., Weber, M.: Monads with arities and their associated theories. J. Pure Appl. Algebra 216, 2029–2048 (2012). arXiv:1101.3064 Gallo, G., Longo, G., Pallottino, S., Nguyen, S.: Directed hypergraphs and applications. Discrete Appl. Math. 42, 177–201 (1993) Gálvez-Carrillo, I., Kock, J., Tonks, A.: Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees. Adv. Math. 254, 79–117 (2014). arXiv:1207.6404 Gan, W.L.: Koszul duality for dioperads. Math. Res. Lett. 10, 109–124 (2003). arXiv:math/0201074 Gepner, D., Kock, J.: Polynomial functors over infinity categories. (in preparation) Getzler, E., Kapranov, M.M.: Modular operads. Compositio Math. 110, 65–126 (1998) Hackney, P., Robertson, M., Yau, D.: Infinity properads and infinity wheeled properads, vol. 2147. Lecture Notes in Mathematics. Springer (2015). arXiv:1410.6716 Joyal, A., Kock, J.: Feynman graphs, and nerve theorem for compact symmetric multicategories (extended abstract). In: Proceedings of the 6th International Workshop on Quantum Physics and Logic (Oxford 2009), vol. 270 of Electronic Notes in Theoretical Computer Science, pp. 105–113, 2011. arXiv:0908.2675 Joyal, A., Moerdijk, I.: A completeness theorem for open maps. Ann. Pure Appl. Logic 70, 51–86 (1994) Kock, J.: Polynomial functors and trees. Internat. Math. Res. Notices 2011, 609–673 (2011). arXiv:0807.2874 Kock, J.: Data types with symmetries and polynomial functors over groupoids. In: Proceedings of the 28th Conference on the Mathematical Foundations of Programming Semantics (Bath, 2012), vol. 286 of Electronic Notes in Theoretical Computer Science, pp. 351–365, 2012. arXiv:1210.0828 Kontsevich, M., Manin, Y.I.: Gromov-Witten classes, quantum cohomology, and enumerative geometry. Commun. Math. Phys. 164, 525–562 (1994) Mac Lane, S.: Categories for the Working Mathematician, second edition. No. 5 in Graduate Texts in Mathematics. Springer-Verlag, New York (1998) Szabo, M.E.: Polycategories. Commun. Algebra 3, 663–689 (1975) Vallette, B.: A Koszul duality for PROPs. Trans. Amer. Math. Soc. 359, 4865–4943 (2007). arXiv:math/0411542 Weber, M.: Generic morphisms, parametric representations and weakly Cartesian monads. Theory Appl. Categories 13, 191–234 (2004) Weber, M.: Familial 2-functors and parametric right adjoints. Theory Appl. Categories 18, 665–732 (2007) Yau, D., Johnson, M.W.: A Foundation for PROPs, Algebras, and Modules. Vol. 203 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI