Talk:Chain duality III (Ex)

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<wikitex>;
<wikitex>;
We check this for objects in $\mathbb A$.
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We check this for objects $M\in\mathbb A$.
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Let $\varphi:TM\to M$ be an element of $M\otimes_{\mathbb A}M$.
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%Then $T_{M,M}\varphi=e_M\circ T\varphi: TM\to T^2M\to M$.
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We have to check the equality of
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$T'_{F(M),F(M)}(F (\varphi) \circ G(M))=e'_{F(M)}\circ T'G(M) \circ T'F(\varphi)$
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and $F(T_{M,M}\varphi)\circ G(M)=F(e_M)\circ FT\varphi\circ G(M)$.
Let $\phi:TM\to M$ be an element of $M\otimes_{\mathbb A}M$.
Then $T_{M,M}\phi=(e_M\circ T\phi: TM\to T^2M\to M$.
</wikitex>
</wikitex>

Revision as of 11:21, 1 June 2012

We check this for objects M\in\mathbb A.

Let \varphi:TM\to M be an element of M\otimes_{\mathbb A}M. %Then T_{M,M}\varphi=e_M\circ T\varphi: TM\to T^2M\to M.

We have to check the equality of T'_{F(M),F(M)}(F (\varphi) \circ G(M))=e'_{F(M)}\circ T'G(M) \circ T'F(\varphi) and F(T_{M,M}\varphi)\circ G(M)=F(e_M)\circ FT\varphi\circ G(M).


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