Tower of objects

In category theory, a branch of abstract mathematics, a tower is defined as follows. Let formula_1 be the poset
of whole numbers in reverse order, regarded as a category. A (countable) tower of objects in a category formula_3 is a functor from formula_1 to formula_3.
In other words, a tower (of formula_3) is a family of objects formula_7 in formula_3 where there exists a map
and the composition
is the map formula_12
Example.
Let formula_13 for some formula_14-module formula_15. Let formula_16 be the identity map for formula_10. Then formula_18 forms a tower of modules.