INTRODUCTION A closed category is determined by thefollowing data: (i) a category y (ii) functors S:VxV -^V and [,]:yopxV-^y (iii) an object I of V (iv) foranyobjects A,B,C ofV , isomorphisms "ABC b A C AB (AKB)JSC -^AS(BSC) ABI -^ A ASB -^ BSA which (as well as their inverses) arenatural inA,Band C (v) foranyobjects A,BofV , arrows dAB : A -^ [B,ABB] eAB : [A,B]BA -• B such that, foranyarrows £:A—- A* andg:B—*-B' ofV , thefollow- ing diagrams arecommutative: d -- [Bf,ABBT] [B,ASBf] -^ A' [B,AHB] EiilHg l £ [B,ABB] [ 1 f j a l ] ^ [B,A f BB] [A f ,B]HA [ f 1 ] i a i - [A,B]BA lHf [Ar,B]SA! [A,B]BA 1 B -^- B [l,g]Bl [A,Bf]SA -^ B'
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