preprint : Investigating The Algebraic Structure of Dihomotopy Types

preprint : Investigating The Algebraic Structure of Dihomotopy Types

[Philippe Gaucher]

Title : Investigating The Algebraic Structure of Dihomotopy Types

Abstract : 
  This presentation is the sequel of a paper published in GETCO'00
  proceedings where a research program to construct an appropriate
  algebraic setting for the study of deformations of higher
  dimensional automata was sketched. This paper will be focused
  precisely on detailing some of its aspects. The main idea is that
  the category of homotopy types can be embedded in a new category of
  dihomotopy types, the embedding being realized by the Globe functor.
  In this latter category, isomorphism classes of objects are exactly
  higher dimensional automata up to deformations leaving invariant
  their computer scientific properties as presence or not of deadlocks
  (or everything similar or related). Some hints to study the
  algebraic structure of dihomotopy types are given, in particular a
  rule to decide whether a statement/notion concerning dihomotopy
  types is or not the lifting of another statement/notion concerning
  homotopy types. This rule does not enable to guess what is the
  lifting of a given notion/statement, it only enables to make the
  verification, once the lifting has been found.
  
Comment : submitted to getco'01. expository paper.

URL : 
http://www-irma.u-strasbg.fr/~gaucher/dihomotopy.ps.gz
http://www-irma.u-strasbg.fr/~gaucher/dihomotopy.pdf