Past and Future as adjoints

[timelets]

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In a two-level past-future transition, we get two different transition functions f (what is going to be there) and g (what is not going to be there). We also get two triples of adjoint functors, depending on how we construct a fibered domain of the past (product vs coproduct).

Lower-level past and future are modeled as exponential objects.

Set^past -> Set^future