@TechReport{Kahl-1997b,
  author = 	 {Wolfram Kahl},
  title = 	 {A Fibred Approach to Rewriting ---
                  How the Duality between Adding and Deleting
                  Cooperates with the Difference between Matching and Rewriting},
  institution =  {Fakult\"at f\"ur Informatik,
                  Universit\"at der Bundeswehr M\"unchen},
  year = 	 1997,
  number = 	 9702,
  month = 	 MAY,
  abstract =  {We present a new approach to rewriting obtained by
		  enhancing and unifying existing variants inside the
		  algebraic (or better categorical) approach to
		  (graph) rewriting. Our approach is motivated by
		  second-order term graph rewriting and stresses on
		  one hand the two-step nature of rule application
		  consisting of deleting and adding items and on the
		  other hand the heterogeneous nature of the rewriting
		  setup where rule steps should be clearly
		  distinguished from matching of rule sides into redexes.

		  Complementing the existing opfibration approach with
		  a dual fibration step turns out to yield a natural
		  and flexible approach with useful new
		  applications. The resulting fibred approach takes
		  advantage of the heterogeneous setting and
		  appropriately reflects the duality between deleting
		  and adding in the course of rewriting, in contrast
		  with the double-pushout approach which simplifies
		  this duality into a symmetry. An important
		  contribution is the universal characterisation of
		  the host object, which has to be found as a
		  pushout-complement in the double pushout
		  approach. 

		  The fibred approach is presented in
		  abstract and independent from any concrete
		  application categories in the manner of High-Level
		  Replacement Systems. Our original motivation for the
		  development of the fibred approach comes from term
		  graphs with bound variables where all other
		  approaches failed; in this paper we present an
		  unusual view on term rewriting as running example.}
}