Homomorphism in each coordinate implies cocycle for trivial group action
Suppose is a group and is an abelian group. Suppose is a function with the property that, for all , if we fix the entries in all coordinates but the coordinate, the induced function from to is a homomorphism of groups.
Then, is a -cocycle for trivial group action.
|What being a homomorphism in each coordinate means||What being a -cocycle means||Link to -cocycle page|
|1||being a homomorphism of groups from to||being a homomorphism of groups from to||--|
|2||satisfies, for all , both of these: and||satisfies, for all , the following:||2-cocycle for trivial group action|
|3||satisfies, for all , all of these:||satisfies, for all , the following:||3-cocycle for trivial group action|