Adjoint functor theorems for lax-idempotent pseudomonads

ARKOR, Nathanael Amariah, Ivan DI LIBERTI and Fosco LOREGIAN. Adjoint functor theorems for lax-idempotent pseudomonads. Theory and Applications of Categories. Mount Allison University, 2024, vol. 41, No 20, p. 667-685. ISSN 1201-561X.

Basic information

Original name

Adjoint functor theorems for lax-idempotent pseudomonads

Authors

ARKOR, Nathanael Amariah (826 United Kingdom of Great Britain and Northern Ireland, belonging to the institution), Ivan DI LIBERTI (380 Italy) and Fosco LOREGIAN

Edition

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

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Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Canada

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.500 in 2022

Organization unit

Faculty of Science

UT WoS

001243753800001

Keywords in English

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

Tags

rivok

Tags

International impact, Reviewed

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Abstract

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.