Subdivided interval categories
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In mathematics, more specifically category theory, there exists an important collection of categories denoted [n] for natural numbers . The objects of [n] are the integers , and the morphism set Hom(i,j) for objects is empty if j < i and consists of a single element if .
Subdivided interval categories are very useful in defining simplicial sets. The category whose objects are the subdivided interval categories and whose morphisms are functors is often written Δ and is called the simplicial indexing category. A simplicial set is just a contravariant functor .
[edit] Examples
The category [0] is the one-object, one-morphism category. It is the terminal object in the category of small categories.
The category [1] has two objects and a single morphism between them. If is any category, then is the category of morphisms and commutative squares in .
[edit] References
MacLane, S. Categories for the working mathematician.