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Tower of objects

From Wikipedia, the free encyclopedia

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

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

References

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  • Section 3.5 of Weibel, Charles A. (1994), An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge University Press, ISBN 978-0-521-55987-4