The definition here seems to be "B is a representation of A if A has a causal relationship with B, but a "laggy" one, so that B doesn't always change in tandem with A"
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That seems more general than what I would have picked, which would have more of a categorical flavor ("There's a map between A and B such that the parts of A map to parts of B, and the relationships between parts of A also map to the relationships between parts of B")
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(well, both more and less general; the identity isomorphism fits my definition fine but isn't laggy, and indeed a "map" that's just the territory isn't much of a map
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