2. There are many symmetries embedded in Hohfeld's octonic discrete projective mapping which are really dual quatronic. In a previous lecture we showed how Hohfeld himself perhaps unconsciously missed perfecting his beautiful gem, indicating that he was not fully aware of the deep symmetries of his model.
3. Is it not obvious that Hohfeld's 8 legal relations constitute a set? But sets tell us nothing of dynamic structures; they order but do not inform.
4. In the lecture, we explain how the 8 legal relations as jural opposites and jural correlatives relate to category theory. We dig even deeper and ask why this must be so.
5. We show how the 8 legal relations are idempotent endomaps in the framework of jural opposites of a single human being, ie, in the monadic.
6. To map jural correlatives, however, we must use functors which are defined as morphisms which preserve in a one-for-one correspondence the objects and morphisms of two categories. Or, simply, a functor is a morphism between categories.
7. One big result is that jural correlatives are not idempotent endomaps but rather isomorphic free and forgetful functors between categories of individuals (monads).
8. Not lazily resting on this discovery, we hypothesize (1) that systemic risk and the great cycles of default are left and right adjoints of pre- and post-default subsystems and together form a Dun Scotus-like fourfold cyclic symmetry; and (2) that short cuts through the great cycles of default via tinkering financial regulation only accelerates the centrifugal forces against the good.