# How to understand the diagonal approximation?

In the Brown's book “Cohomology of groups”, chapter 5.1, there is a concept diagonal approximation, maybe that is not a standard definition, I feel something hard to understand it.

The book says that Alexander–Whitney map is a well-known example of the diagonal approximation, that is different with the diagonal map and I can not find some meaning of approximation. I want to know the motivation of it and show it in some examples. Who can help me?

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Brown gives both motivation and an example (in exercise). What is your question, exactly? (Besides "I feel hard to understand it" and "Who can help me?".) – Grigory M Jan 29 '12 at 13:01
Brown's book refers a theorem which says we have a map from a projective resolution to another projective resolution,that is symmetric,but Δ：F→F⊙F is not like this.I guess it should extend one F to F⊙F,but not sure.For the exercise,I do not sure which one I need to check. – Strongart Jan 31 '12 at 10:34
I am not sure what do you need. But you can view it as a simplicial approximation to diagonal map. This was the suggested motivation for it in the lecture notes by J.F.Davis. – random123 Apr 2 '15 at 18:27