Adjoint functor theorems for lax-idempotent pseudomonads

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...

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Bibliographic Details
Published inTheory and applications of categories Vol. 41; no. 20; p. 667
Main Authors Arkor, Nathanael, Di Liberti, Ivan, Loregian, Fosco
Format Journal Article
LanguageEnglish
Published Sackville R. Rosebrugh 01.01.2024
Subjects
2-category
adjoint functor theorem
formal category theory
free cocompletion
KZ-doctrine
lax-idempotent pseudomonad
Mathematical functions
Mathematics
pseudodistributive law
relative adjunction
Theorems
Theoretical mathematics
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Summary: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.
ISSN:1201-561X
1201-561X