2025/06/11 by Umberto Tarantino, Tarantino, Umberto, Joshua Wrigley +1
Mathematics · #03C20 (Secondary) #03G30 #18C20 #18N15 (Primary) 18C15 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2506.09788
openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Many structured categories of interest are most naturally described as algebras for a relative monad, but turn out nonetheless to be algebras for an ordinary monad. We show that, under suitable hypotheses, the left oplax Kan extension of a relative 2-monad on categories yields a pseudomonad having the same category of colax algebras. In particular, we apply this to the study of ultracategories to recover the 'ultracompletion' pseudomonad.