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