2025/12/12 by Berg, Benno van den, Bourke, John, Seip, Paul · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Logic, programming, and type systems
paper · doi:10.48550/arxiv.2512.11692
openalex publication_date 2025/12/12 · openalex created_date 2025/12/16 · openalex updated_date 2026/07/28
Bourke and Garner described how to cofibrantly generate algebraic weak factorisation systems by a small double category of morphisms. However they did not give an explicit construction of the resulting factorisations as in the classical small object argument. In this paper we give such an explicit construction, as the colimit of a chain, which makes the result applicable in constructive settings; in particular, our methods provide a constructive proof that the effective Kan fibrations introduced by Van den Berg and Faber appear as the right class of an algebraic weak factorisation system.