CONTENTS Page Introduction iv Part One: AN ABSTRACT COHERENCE THEOREM FOR CLOSED CATEGORIES ... 1 Part Two: NON-COMMUTATIVE DIAGRAMS IN CLOSED CATEGORIES 13 §1. The main results 14 §2. Extended graphs 18 A. Allowable extended graphs 24 B. Propriety 30 C. Simplicity 41 D. Identifiability 46 E. The operations B and £,_]. 60 §3. The proofs of Theorems 6 and 7 66 A. The closed category Ji 67 B. The proof of Theorem 6 71 C. The proof of Theorem 7 73 Part Three: A FINAL COHERENCE THEOREM FOR CLOSED CATEGORIES ... . 88 References 90 Index of Terminology and Notations 91 iii
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