Monads in double categories

Thomas M. Fiore*, Nicola Gambino, Joachim Kock

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

9 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.

Original languageEnglish
Pages (from-to)1174-1197
Number of pages24
JournalJournal of Pure and Applied Algebra
Issue number6
Publication statusPublished - Jun 2011


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