Polycategories via pseudo-distributive laws
Abstract
In this paper, we give a novel abstract description of Szabo's polycategories. We use the theory of double clubs -- a generalisation of Kelly's theory of clubs to `pseudo' (or `weak') double categories -- to construct a pseudo-distributive law of the free symmetric strict monoidal category pseudocomonad on Mod over itself qua pseudomonad, and show that monads in the `two-sided Kleisli bicategory' of this pseudo-distributive law are precisely symmetric polycategories.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- June 2006
- DOI:
- 10.48550/arXiv.math/0606735
- arXiv:
- arXiv:math/0606735
- Bibcode:
- 2006math......6735G
- Keywords:
-
- Mathematics - Category Theory;
- 18D05;
- 03G30 (Primary);
- 18D50;
- 03B60 (Secondary)
- E-Print:
- 51 pages with XYpic diagrams