Monadic functors forgetful of (dis)inhibited actions

Alexandru Chirvasitu

Theory and applications of categories, Tome 41 (2024), pp. 1536-1556

Résumé

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.

Détail

Publié le : 2024-10-16

Classification : 18C15, 18D20, 18A30, 18A40, 54D35, 54E15, 54A20, 22F05
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