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41 p, 354.0 KB Double adjunctions / Fiore, Thomas M. (University of Michigan-Dearborn. Department of Mathematics and Statistics) ; Gambino, Nicola (Università di Palermo. Dipartimento di Matematica e Applicazioni) ; Kock, Joachim (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Centre de Recerca Matemàtica
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. [...]
Centre de Recerca Matemàtica 2010 (Prepublicacions del Centre de Recerca Matemàtica ; 1000)  

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