The 2-category of species of dynamical patterns
Benedetto Silvestri
Abstract
A new category $\mathfrak{dp}$, called of dynamical patterns addressing a primitive, nongeometrical concept of dynamics, is defined and employed to construct a $2-$category $2-\mathfrak{dp}$, where the irreducible plurality of species of context-depending dynamical patterns is organized. We propose a framework characterized by the following additional features. A collection of experimental settings is associated with any species, such that each one of them induces a collection of experimentally detectable trajectories. For any connector $T$, a morphism between species, any experimental setting $E$ of its target species there exists a set such that with each of its elements $s$ remains associated an experimental setting $T[E,s]$ of its source species, $T[\cdot,s]$ is called charge associated with $T$ and $s$. The vertical composition of connectors is contravariantly represented in terms of charge composition. The horizontal composition of connectors and $2-$cells of $2-\mathfrak{dp}$ is represented in terms of charge transfer. A collection of trajectories induced by $T[E,s]$ corresponds to a collection of trajectories induced by $E$ (equiformity principle). Context categories, species and connectors are organized respectively as $0,1$ and $2$ cells of $2-\mathfrak{dp}$ with factorizable functors via $\mathfrak{dp}$ as $1-$cells and as $2-$cells, arranged themself to form objects of categories, natural transformations between $1-$cells obtained as horizontal composition of natural transformations between the corresponding factors. We operate a nonreductionistic interpretation positing that the physical reality holds the structure of $2-\mathfrak{dp}$, where the fibered category $\mathfrak{Cnt}$ of connectors is the only empirically knowable part....