### Abstract

These are notes for three lectures on higher properads given at a program at the mathematical institute MATRIX in Australia in June 2016. The first lecture covers the case of operads, and provides a brief introduction to the Moerdijk-Weiss theory of dendroidal sets. The second lecture extends the discussion to properads and our work with Donald Yau on graphical sets. These two lectures conclude with models for higher (pr)operads given by an inner horn filling condition. Finally, in the last lecture, we explore some properties of the graphical category and use them to propose a Segal-type model for higher properads.

Original language | English |
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Title of host publication | 2016 MATRIX annals |

Editors | Jan de Gier, Cheryl E. Praeger, Terence Tao |

Place of Publication | Cham |

Publisher | Springer, Springer Nature |

Pages | 351-374 |

Number of pages | 24 |

ISBN (Electronic) | 9783319722993 |

ISBN (Print) | 9783319722986 |

DOIs | |

Publication status | Published - 2018 |

### Publication series

Name | MATRIX Book Series |
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Publisher | Springer Nature |

Volume | 1 |

ISSN (Print) | 2523-3041 |

ISSN (Electronic) | 2523-305X |

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## Cite this

Hackney, P., & Robertson, M. (2018). Lecture notes on infinity-properads. In J. de Gier, C. E. Praeger, & T. Tao (Eds.),

*2016 MATRIX annals*(pp. 351-374). (MATRIX Book Series; Vol. 1). Cham: Springer, Springer Nature. https://doi.org/10.1007/978-3-319-72299-3_18