Kan extensions and lax idempotent pseudomonads. (English) Zbl 1254.18005
Authors’ abstract: We show that colax idempotent pseudomonads and their algebras can be presented in terms of right Kan extensions. Dually, lax idempotent pseudomonads and their algebras can be presented in terms of left Kan extensions. We also show that a distributive law of a colax idempotent pseudomonad over a lax idempotent pseudomonad has a presentation in terms of Kan extensions.
Reviewer: Ali Madanshekaf (Semnan)
MSC:
| 18D05 | Double categories, \(2\)-categories, bicategories and generalizations (MSC2010) |
| 18C15 | Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads |
| 18A40 | Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) |
