In category theory, a branch of abstract mathematics, a tower is defined as follows.
{\displaystyle {\mathcal {I}}}
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
In other words, a tower (of
) is a family of objects
where there exists a map and the composition is the map
be the identity map for
forms a tower of modules.