coextension of scalars
Algebras and modules
Model category presentations
Geometry on formal duals of algebras
A right adjoint to restriction of scalars. The dual notion to extension of scalars .
Here is one special case.
For a ring, write Mod for its category of modules. Write Ab = Mod for the category of abelian groups.
Write for the forgetful functor that forgets the -module structure on a module and just remembers the underlying abelian group .
The functor has a right adjoint
given by sending an abelian group to the abelian group
equipped with the -module struture by which for an element is sent to the element given by
This is called the coextension of scalars along the ring homomorphism .
The unit of the adjunction
is the -module homomorphism
given on by
- H. Fausk, P. Hu, Peter May, Isomorphisms between left and right adjoints (pdf)
Revised on September 11, 2013 20:29:15
by Urs Schreiber