Publication details

Adjoint functor theorems for lax-idempotent pseudomonads

Authors

ARKOR Nathanael Amariah DI LIBERTI Ivan LOREGIAN Fosco

Year of publication 2024
Type Article in Periodical
Magazine / Source Theory and Applications of Categories
MU Faculty or unit

Faculty of Science

Citation
Web http://www.tac.mta.ca/tac/volumes/41/20/41-20abs.html
Keywords adjoint functor theorem; relative adjunction; lax-idempotent pseudomonad; KZ-doctrine; free cocompletion; pseudodistributive law; 2-category; formal category theory
Description 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 ?-adjoint functor theorems for weakly sound classes of weight ?.

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