Monads in double categories

Thomas M. Fiore, Nicola Gambino, Joachim Kock

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)


We extend the basic concepts of Street's formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category Mnd(C) of monads in a double category C and define what it means for a double category to admit the construction of free monads. Our main theorem shows that, under some mild conditions, a double category that is a framed bicategory admits the construction of free monads if its horizontal 2-category does. We apply this result to obtain double adjunctions which extend the adjunction between graphs and categories and the adjunction between polynomial endofunctors and polynomial monads. © 2010 Elsevier B.V..
Original languageEnglish
Pages (from-to)1174-1197
JournalJournal of Pure and Applied Algebra
Issue number6
Publication statusPublished - 1 Jun 2011


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