Towards a Homotopy Type Theory for Law and Finance

1.  Imagine a homotopy diagram for law and finance involving contracts, torts and criminal law, as well as the media, culture, justice, fairness.  The universe of discourse is represented by an oval that looks like the cosmic background radiation map (LOL) and it is divided in half so that we have a starting frame (ideal initial conditions) between one part on the left which is an unjust and unfair society and another part on the right which is a just and fair society.    Criminal litigation is a partition that moves from right to left with the ideal as the central line axis.  Thus, societies can maximize or minimize the unjust-unfair part in relation to the just-fair part.  Each successful prosecution deforms the two parts such that a just-fair prosecution in the unjust-unfair part tends to decrease the unjust-unfair part and increase the just-fair part.  The old way of talking about the connection between the two parts is to call it a "fibration" between "manifolds"--but those are the physicists and maths whizzos who don't have a handle on the niceties of social theories.  Now, the fibration are just functional connections between the two parts, and it turns out, all that you need to know that could ever really happen between the two parts are embedded in the fibration.  In Homotopy Type Theory, the fibrations are the essence of the "covering space" between the two parts.  We can start to work out certain kinds of equivalences.

2.  Now, assume criminal prosecutions are "transport functions" between the two parts of the oval.

3.  Bizarrely, (and this is a big guess) very dense litigation and all forms of risk of loss (default in the widest possible sense) are functors and act as covering spaces between the two parts.

4.  Implication:  you don't need to know the substance of each criminal prosecution, just the fact that it is being done, that deforms the two parts towards or away from the ideal state of society.  

5.  Please note that the term ‘ideal state’ here does not mean Plato’s ideal good state; it means a perfectly continuous geometric construct of the intuition that does not require anything at all except a few arrows and some ovals.