Presheaves over a join restriction category

Daniel Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Just as the presheaf category is the free cocompletion of any small category, there is an analogous notion of free cocompletion for any small restriction category. In this paper, we extend the work on restriction presheaves to presheaves over join restriction categories, and show that the join restriction category of join restriction presheaves is equivalent to some partial map category of sheaves. We then use this to show that the Yoneda embedding exhibits the category of join restriction presheaves as the free cocompletion of any small join restriction category.

Original languageEnglish
Pages (from-to)289-310
Number of pages22
JournalApplied Categorical Structures
Issue number3
Publication statusPublished - Jun 2019


  • Join restriction categories
  • Join restriction presheaves
  • Sheaves
  • Cocompletion

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