Citation
Aaron Ames. "Homotopy Meaningful Hybrid Model Structures". Michael Farber, R . Ghrist, M. Burger, D . Koditschek (eds.), 121-144, American Mathematical Society, 2007.

Abstract
Hybrid systems are systems that display both discrete and continuous behavior and, therefore, have the ability to model a wide range of robotic systems such as those undergoing impacts. The main observation of this paper is that systems of this form relate in a natural manner to very special diagrams over a category, termed hybrid objects. Using the theory of model categories, which provides a method for "doing homotopy theory" on general categories satisfying certain axioms, we are able to understand the homotopy theoretic properties of such hybrid objects in terms of their "non-hybrid" counterparts. Specifically, given a model category, we obtain a "homotopy meaningful" model structure on the category of hybrid objects over this category with the same discrete structure, i.e., a model structure that relates to the original non-hybrid model structure by means of homotopy colimits, which necessarily exist. This paper, therefore, lays the groundwork for "hybrid homotopy theory."

Electronic downloads

• AMSHybridModel.pdf · application/pdf · 439 kbytes

• HTML

  Aaron Ames. <a
  href="http://chess.eecs.berkeley.edu/pubs/262.html"
  ><i>Homotopy Meaningful Hybrid Model
  Structures</i></a>, Michael Farber, R . Ghrist,
  M. Burger, D . Koditschek (eds.), 121-144, American
  Mathematical Society, 2007.

• Plain text

  Aaron Ames. "Homotopy Meaningful Hybrid Model
  Structures". Michael Farber, R . Ghrist, M. Burger, D .
  Koditschek (eds.), 121-144, American Mathematical Society,
  2007.

• BibTeX

  @inbook{Ames07_HomotopyMeaningfulHybridModelStructures,
      author = {Aaron Ames},
      editor = {Michael Farber, R . Ghrist, M. Burger, D .
                Koditschek},
      title = {Homotopy Meaningful Hybrid Model Structures},
      pages = {121-144},
      publisher = {American Mathematical Society},
      year = {2007},
      abstract = {Hybrid systems are systems that display both
                discrete and continuous behavior and, therefore,
                have the ability to model a wide range of robotic
                systems such as those undergoing impacts. The main
                observation of this paper is that systems of this
                form relate in a natural manner to very special
                diagrams over a category, termed hybrid objects.
                Using the theory of model categories, which
                provides a method for "doing homotopy theory" on
                general categories satisfying certain axioms, we
                are able to understand the homotopy theoretic
                properties of such hybrid objects in terms of
                their "non-hybrid" counterparts. Specifically,
                given a model category, we obtain a "homotopy
                meaningful" model structure on the category of
                hybrid objects over this category with the same
                discrete structure, i.e., a model structure that
                relates to the original non-hybrid model structure
                by means of homotopy colimits, which necessarily
                exist. This paper, therefore, lays the groundwork
                for "hybrid homotopy theory."},
      URL = {http://chess.eecs.berkeley.edu/pubs/262.html}
  }
  

Posted by Aaron Ames on 16 May 2007.
Groups: chess
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