### Abstract

We study a certain type of action of categories on categories and on operads. Using the structure of the categories Delta and Omega governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard group actions on categories and on operads.

Original language | English |
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Pages (from-to) | 193-222 |

Number of pages | 30 |

Journal | Fundamenta Mathematicae |

Volume | 228 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 |

Externally published | Yes |

### Keywords

- Reedy categories
- group actions
- (infinity, 1)-categories
- (infinity, 1)-operads

## Cite this

Bergner, J. E., & Hackney, P. (2015). Reedy categories which encode the notion of category actions.

*Fundamenta Mathematicae*,*228*(3), 193-222. https://doi.org/10.4064/fm228-3-1