Tower of objects
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 (countable) tower of objects in a category  is a functor from  to . In other words, a tower (of ) is a family of objects  in  where there exists a map
 if 
and the composition

is the map

Example 

Let  for some -module . Let  be the identity map for . Then  forms a tower of modules. References
Section 3.5 of 

Category theory