Geodesic
Colax adjunctions and lax-idempotent pseudomonads
Theory and applications of categories, Tome 44 (2025), pp. 227-271.

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We prove a generalization of a theorem of Bunge and Gray about forming colax adjunctions out of relative Kan extensions and apply it to the study of the Kleisli 2-category for a lax-idempotent pseudomonad. For instance, we establish the weak completeness of the Kleisli 2-category and describe colax change-of-base adjunctions between Kleisli 2-categories. Our approach covers such examples as the bicategory of small profunctors and the 2-category of lax triangles in a 2-category. The duals of our results provide lax analogues of classical results in two-dimensional monad theory: for instance, establishing the weak cocompleteness of the 2-category of strict algebras and lax morphisms and the existence of colax change-of-base adjunctions.
Publié le :
Classification : 18N10, 18N15, 18D60, 18D65, 18C20
Keywords: 2-category, lax adjunction, lax-idempotent pseudomonad, KZ-pseudomonad 
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     author = {Miloslav \v{S}t\v{e}p\'an},
     title = {Colax adjunctions and lax-idempotent pseudomonads},
     journal = {Theory and applications of categories},
     pages = {227--271},
     publisher = {mathdoc},
     volume = {44},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2025_44_a6/}
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Miloslav Štěpán. Colax adjunctions and lax-idempotent pseudomonads. Theory and applications of categories, Tome 44 (2025), pp. 227-271. http://geodesic.mathdoc.fr/item/TAC_2025_44_a6/