INDEX OF TERMINOLOGY AND NOTATIONS The numbers give the pages where the definitions may be found. abstract allowable natural transformation, xi allowable (or, canonical) arrow, v,vi allowable E-graph, 24-25 allowable natural transformation, v,xi allowable natural transformation (between shapes), xi allowable natural transformation (with respect to V), v canonical arrow, vi central E-graph, 25 central natural transformation, xiii closed category, iv component (of an allowable natural transformation),xii constant, viii,19 constant functor I, vi constructible E-graph, 27 cut elimination property, xiv cut elimination theorem (for allowable natural transformations),xv,xvi direct component, 71,79 E-graph, 19 entry, 19 expanded instance of .. . , x extended graph, 19 form S, xv,54 form ir , xv form , xv form *, 54 formal arrow between shapes, ix-x -1 -1 formal components (in $ of a,a ,b,b ,c,d,e), 22 formal identity arrow (of a shape) , ix formal instance of a,a ,b,b ,c,d,e, ix graph, vi,viii,xii iterated S-product, xvi identifiable E-graphs, 53 pre-identifiable E-graphs, 47 prime factor (of a shape), xv,25 prime shape, xv,25 91

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