Double ad junctions and free monads

Thomas M. Fiore, Nicola Gambino, Joachim Kock

Research output: Contribution to journalArticlepeer-review


The authors 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. They improve upon their earlier results 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. They also prove that a double category admits Eilenberg-Moore objects if and only if a certain parameterized presheaf is representable. Along the way, they develop parameterized presheaves on double categories and prove a double-categorical Yoneda Lemma.
Original languageEnglish
Pages (from-to)242-307
Number of pages66
JournalCahiers de Topologie et Geometrie Differentielle Categoriques
Issue number4
Publication statusPublished - 2012


  • Double categories
  • adjunctions
  • monads
  • free monads
  • folding
  • cofolding
  • parameterized presheaf
  • Yoneda
  • Eilenberg-Moore


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