Sifted Colimits, Strongly Finitary Monads and Continuous Algebras

2023/01/13 by Jiřı́ Adámek, Adámek, Jiří, Matěj Dostál +3
Mathematics · Medicine · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications

paper · pdf · doi:10.48550/arxiv.2301.05730

openalex publication_date 2023/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We characterize strongly finitary monads on categories Pos, CPO and DCPO as precisely those preserving sifted colimits. Or, equivalently, enriched finitary monads preserving reflexive coinserters. We study sifted colimits in general enriched categories. For CPO and DCPO we characterize varieties of continuous algebras as precisely the monadic categories for strongly finitary monads.

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