Adjoint functor theorems for lax-idempotent pseudomonads

J 2024

Adjoint functor theorems for lax-idempotent pseudomonads

ARKOR, Nathanael Amariah, Ivan DI LIBERTI a Fosco LOREGIAN

Základní údaje

Originální název

Adjoint functor theorems for lax-idempotent pseudomonads

Autoři

ARKOR, Nathanael Amariah (826 Velká Británie a Severní Irsko, domácí), Ivan DI LIBERTI (380 Itálie) a Fosco LOREGIAN

Vydání

Theory and Applications of Categories, Mount Allison University, 2024, 1201-561X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Kanada

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.500 v roce 2022

Organizační jednotka

Přírodovědecká fakulta

UT WoS

001243753800001

Klíčová slova anglicky

adjoint functor theorem; relative adjunction; lax-idempotent pseudomonad; KZ-doctrine; free cocompletion; pseudodistributive law; 2-category; formal category theory

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 15. 7. 2024 16:23, Mgr. Marie Šípková, DiS.

Anotace

V originále

For each pair of lax-idempotent pseudomonads R and I, for which I is locally fully faithful and R distributes over I, we establish an adjoint functor theorem, relating R-cocontinuity to adjointness relative to I. This provides a new perspective on the nature of adjoint functor theorems, which may be seen as methods to decompose adjointness into cocontinuity and relative adjointness. As special cases, we recover variants of the adjoint functor theorem of Freyd, the multiadjoint functor theorem of Diers, and the pluriadjoint functor theorem of Solian-Viswanathan, as well as the adjoint functor theorems for locally presentable categories. More generally, we recover enriched Φ-adjoint functor theorems for weakly sound classes of weight Φ.

Citovat

ARKOR, Nathanael Amariah, Ivan DI LIBERTI a Fosco LOREGIAN. Adjoint functor theorems for lax-idempotent pseudomonads. Theory and Applications of Categories. Mount Allison University, 2024, roč. 41, č. 20, s. 667-685. ISSN 1201-561X.

@article{2418656,
   author = {Arkor, Nathanael Amariah and di Liberti, Ivan and Loregian, Fosco},
   article_number = {20},
   keywords = {adjoint functor theorem; relative adjunction; lax-idempotent pseudomonad; KZ-doctrine; free cocompletion; pseudodistributive law; 2-category; formal category theory},
   language = {eng},
   issn = {1201-561X},
   journal = {Theory and Applications of Categories},
   title = {Adjoint functor theorems for lax-idempotent pseudomonads},
   url = {http://www.tac.mta.ca/tac/volumes/41/20/41-20abs.html},
   volume = {41},
   year = {2024}
}

TY  - JOUR
ID  - 2418656
AU  - Arkor, Nathanael Amariah - di Liberti, Ivan - Loregian, Fosco
PY  - 2024
TI  - Adjoint functor theorems for lax-idempotent pseudomonads
JF  - Theory and Applications of Categories
VL  - 41
IS  - 20
SP  - 667-685
EP  - 667-685
PB  - Mount Allison University
SN  - 1201561X
KW  - adjoint functor theorem
KW  - relative adjunction
KW  - lax-idempotent pseudomonad
KW  - KZ-doctrine
KW  - free cocompletion
KW  - pseudodistributive law
KW  - 2-category
KW  - formal category theory
UR  - http://www.tac.mta.ca/tac/volumes/41/20/41-20abs.html
N2  - For each pair of lax-idempotent pseudomonads R and I, for which I is locally fully faithful and R distributes over I, we establish an adjoint functor theorem, relating R-cocontinuity to adjointness relative to I. This provides a new perspective on the nature of adjoint functor theorems, which may be seen as methods to decompose adjointness into cocontinuity and relative adjointness. As special cases, we recover variants of the adjoint functor theorem of Freyd, the multiadjoint functor theorem of Diers, and the pluriadjoint functor theorem of Solian-Viswanathan, as well as the adjoint functor theorems for locally presentable categories. More generally, we recover enriched Φ-adjoint functor theorems for weakly sound classes of weight Φ.
ER  -

ARKOR, Nathanael Amariah, Ivan DI LIBERTI a Fosco LOREGIAN. Adjoint functor theorems for lax-idempotent pseudomonads. \textit{Theory and Applications of Categories}. Mount Allison University, 2024, roč.~41, č.~20, s.~667-685. ISSN~1201-561X.

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