Dear Categorically Inclined, Has anyone transported the Conway Game construction to the categorical setting in such a way that it works over an arbitrary (strong) monad? If so, is there a reference? i've been experimenting with such a beast using the following recipe: 1. poke a hole in the Conway construction making it parametrically polymorphic in an 'atom' type (following an analogy with the relationship between ZF Set Theory and Fraenkl-Mostowski Set Theory) 2. use the monad to 'collect' the left and right components resulting in a domain eqn CG[M,A] = M[CG[M,A] + A] x M[CG[M,A] + A] For this to work out well enough to support the definitions of the field operations there have to be a few extra maps lying around and some coherence conditions on them. Maybe there's a simpler way to wire up this machine. If so, i'd love a reference. Or, maybe there's a flaw in approach, in which case i'd love to be enlightened. Best wishes, --greg -- L.G. Meredith Managing Partner Biosimilarity LLC 7329 39th Ave SW Seattle, WA 98136 +1 206.650.3740 http://biosimilarity.blogspot.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]