Relative monadicity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00141952" target="_blank" >RIV/00216224:14310/25:00141952 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0021869324005167" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0021869324005167</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2024.08.040" target="_blank" >10.1016/j.jalgebra.2024.08.040</a>

Result language
angličtina
Original language name
Relative monadicity
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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