Simplicial category

In mathematics, the simplicial category Δ is the small category with objects the ordered sets

[n]=\{0<1<2<\ldots<n\}

for each n\geq 0, and morphisms are monotonic non-decreasing functions. It is used to define the concept of a simplicial object, and so also simplicial sets.

Its morphisms are generated by those that 'skip' or 'add' a single elememt of [n]; the detailed relations amongst those mappings therefore underlie large parts of the topological applications.

There's also a geometric interpretation in the form of a functor from Δ into \mathbf{Top}.



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