functoriality of the Burnside ring
We wish to show how the Burnside ring can be turned into a contravariant functor from the category
of finite groups
into the category of commutative
, unital rings.
Let and be finite groups. We already know how acts on objects of the category of finite groups. Assume that is a group homomorphism. Furthermore let be a -set. Then can be naturally equiped with a -set structure
via function:
The set equiped with this group action will be denoted by .
Therefore a group homomorphism induces a ring homomorphism
such that
One can easily check that this turns into a contravariant functor.
Title | functoriality of the Burnside ring |
---|---|
Canonical name | FunctorialityOfTheBurnsideRing |
Date of creation | 2013-03-22 18:08:06 |
Last modified on | 2013-03-22 18:08:06 |
Owner | joking (16130) |
Last modified by | joking (16130) |
Numerical id | 5 |
Author | joking (16130) |
Entry type | Derivation |
Classification | msc 16S99 |