2024/04/19 by Alexandru Chirvăsitu, Chirvasitu, Alexandru · 1 citation
Mathematics · #18A30 #18A40 #18C15 #18D20 #22F05 #54A20 #54D35 #54E15 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2404.13169
openalex publication_date 2024/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We prove a number of results of the following common flavor: for a category C of topological or uniform spaces with all manner of other properties of common interest (separation / completeness / compactness axioms), a group (or monoid) \mathbbG equipped with various types of topological structure (topologies, uniformities) and the corresponding category C^\mathbbG of appropriately compatible \mathbbG-flows in C, the forgetful functor C^\mathbbG→ C is monadic. In all cases of interest the domain category C^\mathbbG is also cocomplete, so that results on adjunction lifts along monadic functors apply to provide equivariant completion and/or compactification functors. This recovers, unifies and generalizes a number of such results in the literature due to de Vries, Mart'yanov and others on existence of equivariant compactifications / completions and cocompleteness of flow categories.