Abstract
Default invariance is the idea that default does not change at any scale of law and finance. Default is a conserved quantity in a universe where fundamental principles of law and finance operate. It exists at the micro-level as part of the fundamental structure of every financial transaction, and at the macro-level, as a fixed critical point within the relatively stable phases of the law and finance cycle. A key point is that default is equivalent to maximizing uncertainty at the micro-level and at the macro-level, is equivalent to the phase transition where unbearable fluctuations occur in all forms of risk transformation, including maturity, liquidity and credit. As such, default invariance is the glue that links the micro and macro structures of law and finance. In this essay, we apply naïve category theory (NCT), a type of mapping logic, to these types of phenomena. The purpose of using NCT is to introduce a rigorous (but simple) mathematical methodology to law and finance discourse and to show that these types of structural considerations are of prime practical importance and significance to law and finance practitioners. These mappings imply a number of novel areas of investigation. From the micro-structure, three macro-approximations are implied. These approximations form the core analytical framework which we will use to examine the phenomena and hypothesise rules governing law and finance. Our observations from these approximations are grouped into five findings. While the entirety of the five findings can be encapsulated by the three approximations, since the intended audience of this paper is the non-specialist in law, finance and category theory, for ease of access we will illustrate the use of the mappings with relatively common concepts drawn from law and finance, focusing especially on financial contracts, derivatives, Shadow Banking, credit rating agencies and credit crises