Chain duality III (Ex)
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Let be a functor of additive categories with chain duality. Show that the assignment
![\displaystyle M \otimes_{\Aa} N \rightarrow F(M) \otimes_{\Aa'} F(N)](/images/math/f/7/1/f71a6dc323f373a316a3880a84f27a5c.png)
given by
![\displaystyle \varphi \colon TM \rightarrow N \quad \mapsto \quad F (\varphi) \circ G(M) \colon T' F (M) \rightarrow FT(M) \rightarrow F(N)](/images/math/3/7/e/37ecfc53a32af5a675fa3ed1d2a9a2b0.png)
induces a -equivariant chain map
![\displaystyle C \otimes_{\Aa} C \rightarrow F(C) \otimes_{\Aa'} F(C)](/images/math/3/0/3/30329794222de4c8ccfa736f372b7cc6.png)
for any .