2018/01/23 by Daniel Lin, Lin, Daniel
Mathematics · #18B99 #2-category #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Artificial intelligence #Category Theory (math.CT) #Closed category #Combinatorics #Computer science #Embedding #FOS: Mathematics #Functor #Homotopy and Cohomology in Algebraic Topology #Join (topology) #Mathematics #Pure mathematics #math.CT #msc:18B99
paper · pdf · doi:10.48550/arxiv.1801.07390
published in arXiv (Cornell University) (Cornell University)
arxiv created 2018/01/23 · openalex publication_date 2018/01/23 · arxiv updated 2018/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.