The formal theory of relative monads

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00135820" target="_blank" >RIV/00216224:14310/24:00135820 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022404924000732" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022404924000732</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2024.107676" target="_blank" >10.1016/j.jpaa.2024.107676</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The formal theory of relative monads

Popis výsledku v původním jazyce

We develop the theory of relative monads and relative adjunctions in a virtual equipment, extending the theory of monads and adjunctions in a 2-category. The theory of relative comonads and relative coadjunctions follows by duality. While some aspects of the theory behave analogously to the non-relative setting, others require new insights. In particular, the universal properties that define the algebra object and the opalgebra object for a monad in a virtual equipment are stronger than the classical notions of algebra object and opalgebra object for a monad in a 2-category. Inter alia, we prove a number of representation theorems for relative monads, establishing the unity of several concepts in the literature, including the devices of Walters, the j-monads of Diers, and the relative monads of Altenkirch, Chapman, and Uustalu. A motivating setting is the virtual equipment V-Cat of categories enriched in a monoidal category V, though many of our results are new even for V = Set.

Název v anglickém jazyce

The formal theory of relative monads

Popis výsledku anglicky

We develop the theory of relative monads and relative adjunctions in a virtual equipment, extending the theory of monads and adjunctions in a 2-category. The theory of relative comonads and relative coadjunctions follows by duality. While some aspects of the theory behave analogously to the non-relative setting, others require new insights. In particular, the universal properties that define the algebra object and the opalgebra object for a monad in a virtual equipment are stronger than the classical notions of algebra object and opalgebra object for a monad in a 2-category. Inter alia, we prove a number of representation theorems for relative monads, establishing the unity of several concepts in the literature, including the devices of Walters, the j-monads of Diers, and the relative monads of Altenkirch, Chapman, and Uustalu. A motivating setting is the virtual equipment V-Cat of categories enriched in a monoidal category V, though many of our results are new even for V = Set.

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

2024

Kód důvěrnosti údajů

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

Název periodika

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

1873-1376

Svazek periodika

228

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

107

Strana od-do

1-107

Kód UT WoS článku

001223882300001

EID výsledku v databázi Scopus

2-s2.0-85189487441