6533b825fe1ef96bd1281e2e

RESEARCH PRODUCT

Monads in double categories

Nicola GambinoNicola GambinoJoachim KockThomas M. Fiore

subject

PolynomialPure mathematicsDemostració Teoria de la02 engineering and technology01 natural sciences510 - Consideracions fonamentals i generals de les matemàtiquesdouble categoriesDistributive law between monadsComputer Science::Logic in Computer ScienceMathematics::Category TheoryFOS: Mathematics0202 electrical engineering electronic engineering information engineeringCategory Theory (math.CT)0101 mathematicsMathematicsDiscrete mathematicsAlgebra and Number TheoryTheory010102 general mathematicsMathematics - Category Theory16. Peace & justiceAdjunctionBicategorySettore MAT/02 - AlgebraCategories (Matemàtica)Monad020201 artificial intelligence & image processing18D05 18C15

description

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.

yearjournalcountryeditionlanguage
2010-01-01Journal of Pure and Applied Algebra
10.1016/j.jpaa.2010.08.003http://dx.doi.org/10.1016/j.jpaa.2010.08.003