Reedy categories which encode the notion of category actions

Julia E. Bergner*, Philip Hackney

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω 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 languageEnglish
Pages (from-to)193-222
Number of pages30
JournalFundamenta Mathematicae
Issue number3
Publication statusPublished - 2015
Externally publishedYes


  • Reedy categories
  • group actions
  • ( ∞, 1)-categories
  • (∞, 1)-operads


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