Distributive laws between monads (triples) were defined by Jon Beck in the 1960s; see [1]. They were generalized to monads in 2-categories and noticed to be monads in a 2-category of monads; see [2]. Mixed distributive laws are comonads in the 2-category of monads [3]; if the comonad has a right adjoint monad, the mate of a mixed distributive law is an ordinary distributive law. Particular case...

The voting patterns of the nine justices on United States Supreme Court continue to fascinate and perplex observers Court. While it is commonly understood that division into a liberal branch conservative inevitably drives many case outcomes, there are finer, less transparent divisions within these two main branches have proven difficult extract empirically. This study imports methods from evolu...

We give a categorical perspective on various product rules, including Brzozowski’s product rule ((st)a = sat + o(s)ta) and the familiar rule of calculus ((st)a = sat+ sta). It is already known that these product rules can be represented using distributive laws, e.g. via a suitable quotient of a GSOS law. In this paper, we cast these product rules into a general setting where we have two monads ...

This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to...

In the United States, Supreme Court justices often vote along ideological lines. Why this is case remains incompletely understood. To learn more about justices’ preferences and nature of decision-making in Court, we differentiate between votes that were pivotal those not. We find situations which a justice pivotal, her ideology even predictive than usual, especially when choice matters for unam...