Colax adjunctions and lax-idempotent pseudomonads
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | Theory and Applications of Categories |
| MU Faculty or unit | |
| Citation | |
| web | http://www.tac.mta.ca/tac/volumes/44/7/44-07abs.html |
| Keywords | 2-category; lax adjunction; lax-idempotent pseudomonad; KZ-pseudomonad |
| Description | 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. |
| Related projects: |