Title:
|
Double adjunctions
|
Author:
|
Fiore, Thomas M.; Gambino, Nicola; Kock, Joachim; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
|
Abstract:
|
We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg-Moore objects in double categories. We improve upon an earlier result of Fiore-Gambino-Kock in [7] to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category horizontally and vertically, and also in its vertical 2-category. We also prove that a double category admits Eilenberg-Moore objects if and only if a certain parameterized presheaf is representable. Along the way, we develop parameterized presheaves on double categories and prove a double Yoneda Lemma. |
Subject(s):
|
-Categories (Matemàtica) |
Rights:
|
open access
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús
https://creativecommons.org/licenses/by-nc-nd/2.5/ |
Document type:
|
Article Prepublicació |
Published by:
|
Centre de Recerca Matemàtica
|
Share:
|
|
Uri:
|
https://ddd.uab.cat/record/76267
|