781 

   781 

   782 There are two alternatives for the next axiom, according whether we are defining

   782 There are two alternatives for the next axiom, according whether we are defining

   783 modules for plain $n$-categories or $A_\infty$ $n$-categories.

   783 modules for plain $n$-categories or $A_\infty$ $n$-categories.

   784 In the plain case we require

   784 In the plain case we require

   785 

   785 

   787 {Let $M$ be a marked $n$-ball and $f: M\to M$ be a homeomorphism which restricts

   787 {Let $M$ be a marked $n$-ball and $f: M\to M$ be a homeomorphism which restricts

   788 to the identity on $\bd M$ and is extended isotopic (rel boundary) to the identity.

   788 to the identity on $\bd M$ and is extended isotopic (rel boundary) to the identity.

   789 Then $f$ acts trivially on $\cM(M)$.}

   789 Then $f$ acts trivially on $\cM(M)$.}

   790 

   790 

   791 \nn{need to rephrase this, since extended isotopies don't correspond to homeomorphisms.}

   791 \nn{need to rephrase this, since extended isotopies don't correspond to homeomorphisms.}