Publication details
KZ-PSEUDOMONADS AND KAN INJECTIVITY Dedicated to the memory of Marta Bunge (1938-2022)
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Article in Periodical |
| Magazine / Source | Theory and Applications of Categories |
| MU Faculty or unit | |
| Citation | |
| web | http://www.tac.mta.ca/tac//volumes/40/16/40-16.pdf |
| Keywords | 2-category; Kan injectivity; KZ-pseudomonad; small object argument |
| Description | We introduce the notion of Kan injectivity in 2-categories and study its properties. For an adequate 2-category K, we show that every set of morphisms H induces a KZ-pseudomonad on K whose 2-category of pseudoalgebras is the locally full sub-2-category of all objects (left) Kan injective with respect to H and morphisms preserving Kan extensions. The main ingredient is the construction of a (pseudo)chain whose appropriate “convergence” is ensured by a small object argument. |