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) G equipped with various types of topological structure (topologies, uniformities) and the corresponding category C^G of appropriately compatible G-flows in C, the forgetful functor C^G → C is monadic. In all cases of interest the domain category C^G 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.
Keywords: Tychonoff space, adjoint functor theorem, bounded flow, closed category, cocomplete, compactification, compactly generated, completion, concrete category, enriched category, exponentiable, flow, internal group, jointly continuous, monadic, monoidal category, monoidal functor, quasi-bounded flow, reflective, separately continuous, solution-set condition, split coequalizer, tripleability, uniformity
@article{TAC_2024_41_a43,
author = {Alexandru Chirvasitu},
title = {Monadic functors forgetful of (dis)inhibited actions},
journal = {Theory and applications of categories},
pages = {1536--1556},
year = {2024},
volume = {41},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a43/}
}
Alexandru Chirvasitu. Monadic functors forgetful of (dis)inhibited actions. Theory and applications of categories, Tome 41 (2024), pp. 1536-1556. http://geodesic.mathdoc.fr/item/TAC_2024_41_a43/