3249 shows the intertwiners we need.

  3249 shows the intertwiners we need.

  3250 Each decorated 2-ball in that figure determines a representation of the 1-category associated to the decorated circle

  3250 Each decorated 2-ball in that figure determines a representation of the 1-category associated to the decorated circle

  3251 on the boundary.

  3251 on the boundary.

  3252 This is the 3-dimensional part of the data for the Morita equivalence.

  3252 This is the 3-dimensional part of the data for the Morita equivalence.

  3253 (Note that, by symmetry, the $c$ and $d$ arrows of Figure \ref{morita-fig-2} 

  3253 (Note that, by symmetry, the $c$ and $d$ arrows of Figure \ref{morita-fig-2} 

  3255 

  3255 

  3256 In order for these 3-morphisms to be equivalences, 

  3256 In order for these 3-morphisms to be equivalences, 

  3257 they must be invertible (i.e.\ $a=b\inv$, $c=d\inv$, $e=f\inv$) and in addition

  3257 they must be invertible (i.e.\ $a=b\inv$, $c=d\inv$, $e=f\inv$) and in addition

  3258 they must satisfy identities corresponding to Morse cancellations on 2-manifolds.

  3258 they must satisfy identities corresponding to Morse cancellations on 2-manifolds.

  3259 These are illustrated in Figure \ref{morita-fig-3}.

  3259 These are illustrated in Figure \ref{morita-fig-3}.