Algebras and modules
Model category presentations
Geometry on formal duals of algebras
Thoughout let be some ring. Write Mod for the category of module over . Write Set for the forgetful functor that sends a module to its underlying set.
For a submodule, the quotient module is the quotient group of the underlying groups, equipped with the -action induced by that on .
The quotient module is equivalently the cokernel of the inclusion in Mod
The quotient module is equivalently the quotient object of the congruence given by projection on the first factor and by addition in .
Revised on December 22, 2015 15:02:32
by Urs Schreiber