Chain duality III (Ex)
From Manifold Atlas
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− | Let $F | + | Let $F : \Aa \rightarrow \Aa'$ be a functor of additive categories with chain duality. Show that the assignment |
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M \otimes_{\Aa} N \rightarrow F(M) \otimes_{\Aa'} F(N) | M \otimes_{\Aa} N \rightarrow F(M) \otimes_{\Aa'} F(N) | ||
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given by | given by | ||
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− | \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 |
Latest revision as of 17:59, 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 .