# Chain duality III (Ex)

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given by | given by | ||

$$ | $$ | ||

− | \varphi \colon TM \rightarrow N \quad \mapsto \quad | + | \varphi \colon TM \rightarrow N \quad \mapsto \quad F (\varphi) \circ G(M) \colon T' F (M) \rightarrow FT(M) \rightarrow F(N) |

$$ | $$ | ||

induces a $\Zz_2$-equivariant chain map | induces a $\Zz_2$-equivariant chain map |

## Revision as of 11:05, 1 June 2012

Let be a functor of additive categories with chain duality. Show that the assignment

given by

induces a -equivariant chain map

for any .