Poly-categories via spans and monads

Jürgen Koslowski (13/03/02)

Multi-categories, introduced by Lambek in 1969, are known to admit a very elegant global description, where monads are employed at two levels: first the free monoid monad is used to suitably ``skew'' the bicategory of spans nad then monads in the resulting bicategory are considered. A very natural generalization of multi-categories was introduced by Szabo in 1975 poly-categories, however by means of a local definition. We provide the missing global characterization, thereby extending the notion of T-category for a cartesian monad T to situatons where both sides of spans are to be subjected to (possibly different) monads.

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Last modified: Fri Feb 15 09:54:23 EST 2002