The 2-category of species of dynamical patterns
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arXiv
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| Format: | Preprint |
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2015
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| _version_ | 1866929327585624064 |
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| author | Silvestri, Benedetto |
| author_facet | Silvestri, Benedetto |
| contents | 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.... |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1512_02628 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | The 2-category of species of dynamical patterns Silvestri, Benedetto Mathematical Physics Category Theory Operator Algebras 18D05, 18D20, 81R99, 81T99, 83Cxx, 81R15, 81T05, 81T20 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.... |
| title | The 2-category of species of dynamical patterns |
| topic | Mathematical Physics Category Theory Operator Algebras 18D05, 18D20, 81R99, 81T99, 83Cxx, 81R15, 81T05, 81T20 |
| url | https://arxiv.org/abs/1512.02628 |