A functorial approach to analogous molecular systems

Abstract

Functorial models of category theory are powerful tools used in many branches of mathematics, even in various computer languages such as Python, however, on an applied mathematics level, functors can also provide novel approaches and new types of systematizations of interrelations among scientific concepts and representations. In a somewhat simplified way, a functor can be thought of as a mathematical tool doing two things all at once: transforming both sets and mappings between those sets. For example, a functor can establish a connection between one entity, involving two sets and a family of transformations between them, and another entity, also involving some two sets and the family of transformations between those. In other words, such a functor transforms one pair of sets and the relations between them to another pair of sets and the relations between them.Functorial models of category theory are powerful tools used in many branches of mathematics, even in various computer languages such as Python, however, on an applied mathematics level, functors can also provide novel approaches and new types of systematizations of interrelations among scientific concepts and representations. In a somewhat simplified way, a functor can be thought of as a mathematical tool doing two things all at once: transforming both sets and mappings between those sets. For example, a functor can establish a connection between one entity, involving two sets and a family of transformations between them, and another entity, also involving some two sets and the family of transformations between those. In other words, such a functor transforms one pair of sets and the relations between them to another pair of sets and the relations between them.