- #1

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,780

- 12

*"Since the squares commute, there is induced a map Tor(A,B) -->Tor(B,A), [...]"*

How does this follow? The map Tor(A,B)-->[itex]A\otimes F_1[/itex] is the connecting homomorphism coming from the long exact sequence (see (6) and its proof) and Tor(B,A)-->[itex]F_1\otimes A[/itex] is inclusion.

It one starts with an element x of Tor(A,B), then pushes it to [itex]A\otimes F_1[/itex] to an element x' and then to [itex]F_1\otimes A[/itex] to an element x'', there is no guarantee as far as I can see that there will be a y in Tor(B,A) with y=x''...

Thanks for any help.