The following paper is available by anonymous ftp. MODELLING TERM-REWRITING SYSTEMS BY SESQUI-CATEGORIES. Abstract It is well-known that a term rewriting system gives rise to a 2-category in which the objects are finite sets of variables, the morphisms are substitutions, and the 2-cells are rewrites. This paper demonstrates that a generalization of a 2-category, called a sesqui-category, is a more appropriate categorical model for a term rewriting system. This is principally because, unlike the case of a 2-category, the sesqui-category associated to a term rewriting system supports a notion of length on its 2-cells. This notion of length is used in developing definitions of local confluence and critical pair in the context of an arbitrary sesqui-category with length and certain additional structure. The relationship between these abstract definitions and their usual term rewriting counterparts is established. This provides some evidence that sesqui-categories may be an appropriate vehicle for an abstract theory of rewriting capable of handling critical pairs. The paper can be obtained by anonymous ftp from ftp.cs.keele.ac.uk the file is pub/techreports/1994/tr94-02.ps ------------------------------------------------------------------------- John Stell Department of Computer Science email john@cs.keele.ac.uk Keele University Keele, Staffordshire, telephone +44 782 583260 ST5 5BG fax +44 782 713082 U. K. -------------------------------------------------------------------------