Informace o publikaci
Relative monadicity
| Autoři | |
|---|---|
| Rok publikování | 2025 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Journal of Algebra |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://www.sciencedirect.com/science/article/pii/S0021869324005167 |
| Doi | https://doi.org/10.1016/j.jalgebra.2024.08.040 |
| Klíčová slova | Relative monad; Relative adjunction; Monadicity; Virtual equipment; Formal category theory; Enriched category theory; Contents |
| Popis | We establish a relative monadicity theorem for relative monads with dense roots in a virtual equipment, specialising to a relative monadicity theorem for enriched relative monads. In particular, for a dense V-functor j : A-* E, a Vfunctor r: D-* E is j-monadic if and only if r admits a left j-relative adjoint and creates j-absolute colimits. This provides a refinement of the classical monadicity theorem - characterising those categories whose objects are given by those of E equipped with algebraic structure - in which the arities of the algebraic operations are valued in A. In particular, when j = 1, we recover a formal monadicity theorem. Furthermore, we examine the interaction between the pasting law for relative adjunctions and relative monadicity. As a consequence, we derive necessary and sufficient conditions for the (j-relative) monadicity of the composite of a V-functor with a (j-relatively) monadic Vfunctor. |