1352 

  1352 

  1353 We can define marked pinched products $\pi:E\to M$ of marked balls analogously to the 

  1353 We can define marked pinched products $\pi:E\to M$ of marked balls analogously to the 

  1354 plain ball case.

  1354 plain ball case.

  1355 Note that a marked pinched product can be decomposed into either

  1355 Note that a marked pinched product can be decomposed into either

  1356 two marked pinched products or a plain pinched product and a marked pinched product.

  1356 two marked pinched products or a plain pinched product and a marked pinched product.

  1358 

  1358 

  1359 \begin{module-axiom}[Product (identity) morphisms]

  1359 \begin{module-axiom}[Product (identity) morphisms]

  1360 For each pinched product $\pi:E\to M$, with $M$ a marked $k$-ball and $E$ a marked

  1360 For each pinched product $\pi:E\to M$, with $M$ a marked $k$-ball and $E$ a marked

  1361 $k{+}m$-ball ($m\ge 1$),

  1361 $k{+}m$-ball ($m\ge 1$),

  1362 there is a map $\pi^*:\cM(M)\to \cM(E)$.

  1362 there is a map $\pi^*:\cM(M)\to \cM(E)$.