Relative monadicity

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Relative monadicity

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Relative monadicity

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Algebra

ISSN

0021-8693

e-ISSN

1090-266X

Svazek periodika

663

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

36

Strana od-do

399-434

Kód UT WoS článku

001336621500001

EID výsledku v databázi Scopus

2-s2.0-85206291628