Tower (mathematics)


In category theory, a branch of abstract mathematics, a tower is defined as follows. Let be the poset
of whole numbers in reverse order, regarded as a category. A tower of objects in a category is a functor from to.
In other words, a tower is a family of objects in where there exists a map
and the composition
is the map

Example

Let for some -module. Let be the identity map for. Then forms a tower of modules.