Monads in double categories
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Monads in double categories. / Fiore, Thomas M.; Gambino, Nicola; Kock, Joachim.
I: Journal of Pure and Applied Algebra, Bind 215, Nr. 6, 06.2011, s. 1174-1197.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Monads in double categories
AU - Fiore, Thomas M.
AU - Gambino, Nicola
AU - Kock, Joachim
PY - 2011/6
Y1 - 2011/6
N2 - 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. (C) 2010 Elsevier B.V. All rights reserved.
AB - 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. (C) 2010 Elsevier B.V. All rights reserved.
KW - WELLFOUNDED TREES
U2 - 10.1016/j.jpaa.2010.08.003
DO - 10.1016/j.jpaa.2010.08.003
M3 - Journal article
VL - 215
SP - 1174
EP - 1197
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 6
ER -
ID: 331502011