Chain duality V (Ex)

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Let $\Aa$$; Let \Aa be an additive category with chain duality (T,e). Show that under the isomorphism T_{M,TM} \colon M \otimes_{\Aa} TM \rightarrow TM \otimes_{\Aa} M we have T_{M,TM} (\textup{id}) = e_{M}. Observe that e can be defined this way if we have already defined T and T_{M,N}. == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises with solution]]\Aa$ be an additive category with chain duality $(T,e)$$(T,e)$. Show that under the isomorphism

$\displaystyle T_{M,TM} \colon M \otimes_{\Aa} TM \rightarrow TM \otimes_{\Aa} M$

we have

$\displaystyle T_{M,TM} (\textup{id}) = e_{M}.$

Observe that $e$$e$ can be defined this way if we have already defined $T$$T$ and $T_{M,N}$$T_{M,N}$.