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@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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