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 (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

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