0000000000019276

AUTHOR

Thomas M. Fiore

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Monads in double categories

2010

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.

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 18C15Journal of Pure and Applied Algebra
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