Polycategories via pseudo-distributive laws
Category Theory
2008-11-10 v3
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.
Keywords
Cite
@article{arxiv.math/0606735,
title = {Polycategories via pseudo-distributive laws},
author = {Richard Garner},
journal= {arXiv preprint arXiv:math/0606735},
year = {2008}
}
Comments
51 pages with XYpic diagrams; v2: journal version, improvements to Sections 2.2 and 3.2, other minor infelicities corrected; v3: missing appendix reinstated