Coinflation functor on homology
From Groupprops
Definition
Suppose is a group and
is a normal subgroup of
. Suppose
is an abelian group and
is a homomorphism of groups, making
into a
-module. Denote by
the quotient of
by the subgroup of elements of the form
, with
.
Then, the coinflation homomorphism is defined as the composite:
where the first map is the natural map obtained by viewing cohomology as a covariant functor in its second coordinate, applied to the surjection of
-modules, and the second map is obtained by applying the corestriction functor on homology to the quotient map
.