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

for each , 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 element 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 .