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
bA
CAB
(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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