Monads in double categories

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

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

Harvard

Fiore, TM, Gambino, N & Kock, J 2011, 'Monads in double categories', Journal of Pure and Applied Algebra, bind 215, nr. 6, s. 1174-1197. https://doi.org/10.1016/j.jpaa.2010.08.003

APA

Fiore, T. M., Gambino, N., & Kock, J. (2011). Monads in double categories. Journal of Pure and Applied Algebra, 215(6), 1174-1197. https://doi.org/10.1016/j.jpaa.2010.08.003

Vancouver

Fiore TM, Gambino N, Kock J. Monads in double categories. Journal of Pure and Applied Algebra. 2011 jun.;215(6):1174-1197. https://doi.org/10.1016/j.jpaa.2010.08.003

Author

Fiore, Thomas M. ; Gambino, Nicola ; Kock, Joachim. / Monads in double categories. I: Journal of Pure and Applied Algebra. 2011 ; Bind 215, Nr. 6. s. 1174-1197.

Bibtex

@article{fd3f5e3ccb854573ab4557f034529ce0,
title = "Monads in double categories",
abstract = "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.",
keywords = "WELLFOUNDED TREES",
author = "Fiore, {Thomas M.} and Nicola Gambino and Joachim Kock",
year = "2011",
month = jun,
doi = "10.1016/j.jpaa.2010.08.003",
language = "English",
volume = "215",
pages = "1174--1197",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier BV * North-Holland",
number = "6",

}

RIS

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