Talk:Chain duality III (Ex)
From Manifold Atlas
(Difference between revisions)
(One intermediate revision by one user not shown) | |||
Line 1: | Line 1: | ||
<wikitex>; | <wikitex>; | ||
− | + | The most interesting part is to check equivariance, say for objects $M\in\mathbb A$. | |
Let $\varphi:TM\to M$ be an element of $M\otimes_{\mathbb A}M$. | Let $\varphi:TM\to M$ be an element of $M\otimes_{\mathbb A}M$. | ||
Line 16: | Line 16: | ||
FT^2M\ar[r]^{Fe_M}& | FT^2M\ar[r]^{Fe_M}& | ||
F(M) | F(M) | ||
− | } | + | }$$ |
− | + | as the first square commutes by naturality of $G$ and the second one by definition of a | |
+ | functor of categories with chain duality. | ||
</wikitex> | </wikitex> |
Latest revision as of 11:35, 1 June 2012
The most interesting part is to check equivariance, say for objects .
Let be an element of .
We have to check the equality of
and
This follows from the commutative diagram
as the first square commutes by naturality of and the second one by definition of a functor of categories with chain duality.