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H-Categories and Graphs Aaron D. Ames and Paulo Tabuada
 

Summary: H-Categories and Graphs
Aaron D. Ames and Paulo Tabuada
Abstract
H-categories are an essential ingredient of categorical models for hybrid systems. In this note,
we consider oriented H-categories and form the category of these categories, Hcat. The main
result is that there is an isomorphism of categories:
Hcat = Grph.
The proof of this fact is constructive in nature, i.e., it is shown how to obtain a graph from and
H-category and an H-category from a graph.
1. Introduction
Small categories play a critical role in the study of diagrams in a category, i.e., one
often considerers the the functor category TC whose objects are all functors FFF : C
T, for a small category C. Similarly, diagrams can also be defined by a graph whose
vertices index a collection of objects in T and edges index a collection of morphisms
in T. These two notions of "diagrams" in a category are related via functors from
Grph to Cat and Cat to Grph which form an adjoint pair [7]. The disadvantage to
this construction is that the creation of a small category from a graph is achieved
by adding information to the graph (in the form of paths in the graph); it may be
the case that this added information is unwanted and/or unneeded. This motivates
the creation of a small category from a graph in which the resulting category is the

  

Source: Ames, Aaron - Department of Mechanical Engineering, Texas A&M University

 

Collections: Engineering