Polycategories via pseudo-distributive laws

Details Polycategories via pseudo-distributive laws Polycategories via pseudo-distributive laws

2006-06-28

arxiv.org/abs/math/0606735v3

Advances in Mathematics 218 (2008), no. 3, 781--827

Mathematics

Category Theory

51 pages with XYpic diagrams; v2: journal version, improvements to Sections 2.2 and 3.2, other minor infelicities corrected; v

Scientific paper

10.1016/j.aim.2008.02.001

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.

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