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292 m_1 \circ m_3 & = m_2 \circ (\id \tensor m_2) - m_2 \circ (m_2 \tensor \id) - \\ & \qquad - m_3 \circ (m_1 \tensor \id \tensor \id) - m_3 \circ (\id \tensor m_1 \tensor \id) - m_3 \circ (\id \tensor \id \tensor m_1) |
292 m_1 \circ m_3 & = m_2 \circ (\id \tensor m_2) - m_2 \circ (m_2 \tensor \id) - \\ & \qquad - m_3 \circ (m_1 \tensor \id \tensor \id) - m_3 \circ (\id \tensor m_1 \tensor \id) - m_3 \circ (\id \tensor \id \tensor m_1) |
293 \end{align*} |
293 \end{align*} |
294 as required (c.f. \cite[p. 6]{MR1854636}). |
294 as required (c.f. \cite[p. 6]{MR1854636}). |
295 \todo{then the general case.} |
295 \todo{then the general case.} |
296 We won't describe a reverse construction (producing a topological $A_\infty$ category |
296 We won't describe a reverse construction (producing a topological $A_\infty$ category |
297 from a `conventional' $A_\infty$ category), but we presume that this will be easy for the experts. |
297 from a ``conventional" $A_\infty$ category), but we presume that this will be easy for the experts. |