295 In a Moore loop space, we have a separate space $\Omega_r$ for each interval $[0,r]$, and a |
295 In a Moore loop space, we have a separate space $\Omega_r$ for each interval $[0,r]$, and a |
296 {\it strictly associative} composition $\Omega_r\times \Omega_s\to \Omega_{r+s}$. |
296 {\it strictly associative} composition $\Omega_r\times \Omega_s\to \Omega_{r+s}$. |
297 Thus we can have the simplicity of strict associativity in exchange for more morphisms. |
297 Thus we can have the simplicity of strict associativity in exchange for more morphisms. |
298 We wish to imitate this strategy in higher categories. |
298 We wish to imitate this strategy in higher categories. |
299 Because we are mainly interested in the case of strong duality, we replace the intervals $[0,r]$ not with |
299 Because we are mainly interested in the case of strong duality, we replace the intervals $[0,r]$ not with |
300 a product of $k$ intervals (c.f. \cite{0909.2212}) but rather with any $k$-ball, that is, |
300 a product of $k$ intervals (c.f. \cite{ulrike-tillmann-2008,0909.2212}) but rather with any $k$-ball, that is, |
301 any $k$-manifold which is homeomorphic |
301 any $k$-manifold which is homeomorphic |
302 to the standard $k$-ball $B^k$. |
302 to the standard $k$-ball $B^k$. |
303 |
303 |
304 By default our balls are unoriented, |
304 By default our balls are unoriented, |
305 but it is useful at times to vary this, |
305 but it is useful at times to vary this, |