Talk:Chain duality V (Ex)
From Manifold Atlas
This is immediate from the definition that .
We turn the question around and show that . We will suppress all decorations occuring in tensor products and Hom-sets and look at a sequence of maps
Somewhat more elaborate, so that we really can see what's going on:
This sequence of maps is precisely the previously mentioned . (which has hopefully been treated in the solution to exercise 10 on L-groups) Applying this map to , we get , which is equal to the identity map, as part of its very definition.