111 Instead of an ordinary oriented $(n-1)$-manifold via the inward (or outward) normal 

   111 Instead of an ordinary oriented $(n-1)$-manifold via the inward (or outward) normal 

   112 first (or last) convention, perhaps it is better to define the boundary to be an $(n-1)$-manifold

   112 first (or last) convention, perhaps it is better to define the boundary to be an $(n-1)$-manifold

   113 equipped with an orientation of its once-stabilized tangent bundle.

   113 equipped with an orientation of its once-stabilized tangent bundle.

   114 Similarly, in dimension $n-k$ we would have manifolds equipped with an orientation of 

   114 Similarly, in dimension $n-k$ we would have manifolds equipped with an orientation of 

   115 their $k$ times stabilized tangent bundles.

   115 their $k$ times stabilized tangent bundles.

   116 For the moment just stick with unoriented manifolds.}

   118 For the moment just stick with unoriented manifolds.}

   117 \medskip

   119 \medskip

   118 

   120 

   119 We have just argued that the boundary of a morphism has no preferred splitting into

   121 We have just argued that the boundary of a morphism has no preferred splitting into

   120 domain and range, but the converse meets with our approval.

   122 domain and range, but the converse meets with our approval.