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.
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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.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Canada
Confidentiality degree is not subject to a state or trade secret
WWW 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
Changed by Changed by: Mgr. Marie Šípková, DiS., učo 437722. Changed: 15/7/2024 16:23.
Abstract
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.
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