Speaker: Gunjeet Singh (Wayne State University)

Title: Reconstructing One-Dimensional Model Structures from Fibrant and Cofibrant Replacement Data

Abstract: A one-dimensional model category is a model category in which the lifting problems defining its two weak factorization systems have unique solutions. Such factorization systems are called orthogonal factorization systems, and they arise naturally throughout category theory. In this talk, I will present a classification of certain "strong" one-dimensional model structures on locally presentable categories. Given a pair (F, C) consisting of an idempotent monad and an idempotent comonad satisfying suitable compatibility conditions, these data determine a unique strong one-dimensional model structure whose fibrant and cofibrant replacement functors are exactly F and C. Finally, I will give some concrete examples of such model structures arising from closure and interior operators on Boolean algebras. This is ongoing work, largely inspired by previous joint work with Andrew Salch.