The Grothendieck Construction in Categorical Network Theory
arXiv:2101.07777
Abstract
In this thesis, we present a flexible framework for specifying and constructing operads which are suited to reasoning about network construction. The data used to present these operads is called a \emph{network model}, a monoidal variant of Joyal's combinatorial species. The construction of the operad required that we develop a monoidal lift of the Grothendieck construction. We then demonstrate how concepts like priority and dependency can be represented in this framework. For the former, we generalize Green's graph products of groups to the context of universal algebra. For the latter, we examine the emergence of monoidal fibrations from the presence of catalysts in Petri nets.
arXiv commentPh.D. Thesis, 151 pages
References in corpus (13)
- Physics, Topology, Logic and Computation: A Rosetta Stone
- A 2-categories companion
- Homotopy field theory in dimension 3 and crossed group-categories
- Configuration Structures, Event Structures and Petri Nets
- Open Petri Nets
- Duality and traces for indexed monoidal categories
- Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams
- On operads, bimodules and analytic functors
- Linear usage of state
- String diagrams for traced and compact categories are oriented 1-cobordisms
- Generalization of Algebraic Operations via Enrichment
- On Enriched Fibrations
- Noncommutative Network Models