Conway Games over arbitrary (strong) monad?

Conway Games over arbitrary (strong) monad?

[Meredith Gregory]

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


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