Abstract
The article contains a detailed description of the connection between finite depth inclusions of
I
I
1
-subfactors and finite
C
∗
-tensor categories (i.e.
C
∗
-tensor categories with dimension function for which the number of equivalence classes of irreducible objects is finite). The
(N,N)
-bimodules belonging to a
I
I
1
-subfactor
N⊂M
with finite Jones index form a
C
∗
-tensor category with dimension function. Conversely, taking an object of a finite
C
∗
-tensor category C we construct a subfactor
A⊂R
of the hyperfinite
I
I
1
-factor R with finite index and finite depth. For this subfactor we compute the standard invariant and show that the
C
∗
-tensor category of the corresponding
(A,A)
-bimodules is equivalent to a subcategory of C. We illustrate the results for the
C
∗
-tensor category of the unitary finite dimensional corepresentations of a finite dimensional Hopf-*-algebra.