2025/08/20 by E. V. Martyanov, Martyanov, E. V.
Mathematics · #18B25 #18C15 (Secondary) #54B30 (Primary) 18A32 #54E15 #54H15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2508.14981
openalex publication_date 2025/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present work, we investigate the extension of double factorization systems to the categories of Eilenberg-Moore (co)algebras. We show that the double factorization systems (ExEpi,Bim,ExMono) in the categories Tych, Unif and Comp extend to the same double factorization systems in the corresponding categories of Eilenberg-Moore algebras Tychℍt, Unifℍu and Compℍc. We establish a connection between cartesian double factorization systems and LT-topologies. We provide sufficient conditions for the extension of cartesian double factorization systems to the topos of coalgebras.