OAL-RAG 2024: James Madden (LSU)

Title: Posites.
Abstract: A coverage on a category consists of a collection covering families that are stable under pullback. This provides the minimum structure necessary to define a notion of sheaf. In his book, Stone Spaces, Johnstone specialized this notion to meet-semilattices to create a language in which to describe presentations of frames. A meet-semilattice equipped with a coverage is called a posite; see the article ``posite'' at ncatlab.org/. My talk will provide a quick survey of the category of posites, and will describe connections to (a) classical topics on meet-semilattices (such injective hulls), (b) κ -frames, and (c) term rewriting systems.