Isomorphisms and Adjunctions in Corporate Finance Law - Some Speculations

1. In the summer, I usually read (skim read and fill in the margins with messy notes and doodles using a Pilot 0.4 black pen--if i feel artistic, sepia is preferred) a couple textbooks relating to corporate finance law and wonder, gritting my teeth, why these authors haven't studied Hohfeld and Category Theory. I think I know why. It's a sociology of knowledge problem, so a perfectly general field which may be very generally defined ("raising money for a company") is studied in terms of extremely local rules ("limited to the laws of England Wales" or "to the US Federal securities laws and the laws of the state of New York"). The authors will then disclaim except for some purpose of "comparison" any knowledge or relevance of other legal jurisdictions, and off we go looking at and commenting on the law of the land.

2. Here's a radically lazy thought: why not learn Hohfeld and Category Theory enough so that you can translate all of the laws relating to corporate finance law into a couple squiggles?

3. Right off the bat, you'll see intensional and extensional definitions of corporate finance law (the intensional definition asserts a feature common to the phenomena under study, and the extensional definition will list the elements composing the set of phenomena under study). Those who critique black letter law as being low brow scholarship are Intensionalists at heart. But the practitioner doesn't really trust the "impressionistic observations" of the Intensionalists as being of any use to his immediate needs of knowing the Extensionalist definitions of the laws. So, exactly how does the sky meet the tarmac and tarmac meet the sky?

4. Isomorphism for Disclosures of a Prospectus and Adjunction for Universality in Comparative Law. What the Intensionalists and Extensionalists must agree on is the conception of disclosure as being a hard-datum phenomenon under study as well as some normative value and goal of overall corporate finance theory. But what is disclosure per se? Having wandered around various disciplines to bottom out this question, I guess the best and most satisfying answer comes from a confluence of theories including Ramsey's Law, Shannon's Information Theory and some bits (pun intended) from quantum information theory. The short way to get underneath the hood, is to define disclosure in terms of a PHYSICAL TRANSFERENCE in a MUTUALITY transaction. In category theory terms, this looks like: (1) an isomorphism of f:A->B, g:B->A; and ideally, (2) a naturality transformation where we have an adjunction which is really an isomorphism amongst functors. (1) gets you simple disclosures which MUST meet and satisfy Akerloffian boundaries against asymmetric information. (2) gets you to the level of comparative law systems where transactions MUST meet and satisfy the bounds imposed by UNIVERSALITY (as in universal bankruptcy theories) and HARMONISATION by deference (as in EU normative treaties or in conflict of law laws under the old common law). (1) can be illustrated by disentangling a prospectus published under US Securities law or under EU law and asking, "How can we be assured that the materiality of disclosure test has been met?" The positive answer should (and logically must) be that the isomorphism in (1) has been met. (2) is much more open to research. I can see the steps one would need to undertake to make the argument plausible and I'm pretty sure if one could do it, that it would prove to be a big contribution to comparative law theory.