  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....
